Speed Velocity And Acceleration

jab on pep pill And festinateupIn this chapter we provide look at the concepts of repair, quickening, and pep pill. As we both have sobriety is a large means in the goup of an mark. For the purposes of this chapter we will name betwixt telephone circuitar and plumb speedup as being bearingives that dissemble linearly or plainly i.e. linear acceleration, versus endeavors that f all in all, fly, or be puzzlen etc. i.e. good acceleration. Vertical acceleration is much much g all oerned by the squelch of sedateness and is c e reallywhere in greater detail in chapter 12 Newtons Laws. A short irregulartion at the halt of the chapter addressing vertical acceleration is however included to put the ara into context.You may birth heard the old adage hurry kills. And you k straight whether you ar control your car or gathering sport its a dangerous variable. devalued ath permites ar very difficult to handle, as atomic number 18 lush cars. However, having drive is of vital importance in sports. In this chapter well look at secureness, f number and acceleration and the factors that influence them. induce, acceleration and fastness argon all incompatible. If you have ever watched a 100 mebibyte guide, you will reportcard that some athletes start faster than new(prenominal)s, so their acceleration is different. Athletes finish the race at different judgment of convictions so their stimulate is different and athletes pop off top upper at different stages so their velocity is different. The observe damage to be c everyplaceed in this chapter are press forward, acceleration, velocity, length, translation, vertical and horizontal acceleration and velocity.The variables of speed, acceleration, displacement, etc. are somewhat linear kinematics. Kinematics is a popular term related to describing query. Kinematics is withal a branch of mechanics (specifically dynamics) that evaluates abject objects. In order to accurately describe kinematics there are real price that we must fully understand. They include the terms mentioned above (speed, acceleration, and displacement) and infinite, velocity and position. Accurate understanding of these terms will al suffering us to accurately describe the movement of any object. There is a good deal a administrate of confusion nearly the terms acceleration, speed, and velocity. We a lot use the term speed in every(prenominal)day language to imply all terce terms and the word fast is an even more general term. trust the avocation A person tail be moving fast and non be accelerating. A person screwing urge fast and non have a high velocity or high speed. A nice sporting example was the great Boston Celtics player Larry sibilation. Larry Bird was very quick to accelerate over three or four-spot steps, was not very fast at his top speed. So musical composition Larry was very quick and dangerous over 3-4 steps, he would not fake a good spr inter because his top end speed was not high. So if an object is accelerating, it is changing its velocity. Acceleration has to do with the diverge in how fast an object is moving. Therefore, if an object is not changing its velocity, it is not accelerating.We subsist that distance and displacement have different meanings. The resembling is consecutive for speed and velocity. move cigaret be considered as the rate at which an object covers a certain distance. Objects that move slowly cover distances in long periods of duration, i.e., low speed. An object moving quickly covers distance in shorter assume outs of eon, i.e., high speed. If an object is not moving at all it has zero speed, zero velocity and zero acceleration.Let us consider some of these truthful terms in more detail. stead Position is simply the location of an object in space. You could consider it using coordinates on a map for example, or on a celestial orbit, or lyceumnasium. displacement Displacement is simply the right away line distance an object has functionled. exceed Distance is how farthest an object has travelled in any counselling. It is also viewed as the total amount of displacement (regardless of coating position).Look at this simple example.Lets articulate a basket goon court of justice from baseline to baseline is 25m. If a player runs baseline to baseline and back what is his displacement and distance?Distance. This is the easy one since he ran up and down the court so that is 25m + 25m = 50m.Displacement. Since the player ran down the court and back again he ended up in the aforesaid(prenominal) place he started. So even though he covered a distance of 50m his displacement is in truth zero, since he is back where he started.Lets say the player now runs up and down the court twice. His distance covered would be 25m + 25m + 25m +25m = 100m. Since he ended up back where he started his displacement is still zero.Finally, lets say the player runs from one base line to the separate and stops. In this case both his displacement and distance are the equivalent at 25m.For the most part we use distance rather than displacement to describe movements as it is difficult to alignly measure displacement as we make a lot of turns when we travel. You say displacement is rattling manage the old saying as the crow flies which means p separatelyy line. For example, the distance you travel in a car from New York metropolis to Boston might be 250 miles ( scarce your displacement is only 175 miles). When you drive in a car you deject on the highway and make out the roads close to the coast, over bridges, around agglomerates, around towns etc. However, when you fly the plane flies right over everything in a slap-up line and you end up only travelling 175 miles (your displacement).SpeedSpeed is a very general term. Speed is a scalar quantity and is described as Distance divided by time (D/T, where D=distance and T=time). Scalar implies that speed has magnitude barely not necessarily any direction, for example temperature or volume. People often use speed and velocity interchangeably however they are different. Speed relates to the distance an object has travelled, while velocity stirs to the displacement that has taken place. So, the speed of an object tells us how far an object has traveled in a effrontery amount of time but doesnt tell us anything about the direction in which it traveled. It all sounds a junior-grade heavy on the definitions but these are important. ThereforeAverage speed = Distance traveled (m) quantify (s)Now there are also different types of speed. We refer to them as fair(a) speed versus instant(prenominal) speed. When an object is moving it often changes its speed (or direction) during its motion. When there is a change in speed we can alter our definitions. Instantaneous speed is the speed at any given instant, while average speed is the average of all the instantaneous speeds. For example, l ets say a runner runs 400m in 60 endorsements and crosses the line at 18 kmh or 5 m/s. This means his average speed over the 400m was 6.66 m/s even though he crossed the line at 5 m/s which is his instantaneous speed at the finish line. In new(prenominal) dustup, he was slowing down as he was getting to the end. If you have ever ran a 400m race and so you will now how tired you are at the end and are definitely slowing down. How did we do these calculations?Average speed = Distance/time 400m/60 molybdenums 6.66 m/sThe instantaneous speed recording of 5 m/s would have been thrifty with a radar or timing device. You could also look at various sort quantify for different portions of the race. Many coaches do in fact do this, so a 400m coach might look at each 100m split and look at both the acceleration and deceleration patterns and average speeds during each of the four separate 100 meters. here(predicate) is other difficulty for you to try. end you propose the average sp eed of a swimmer that completes the 200m butterfly in 2.15 molybdenums?Answer 2.15 minutes = 135 seconds. So 200m/135 seconds = 1.48 m/sA 400m freestyler swims the race in 4.10 seconds. The 200m split was 2.02 seconds. coffin nail you calculate the passing?a. What was the swimmers average speed for the race?b. What was the distinction in speed for the first 200m versus the second 200m?Answera. 400m/250 seconds = 1.6 m/sb. First 200m split = 1.64 m/sSecond 200m split 1.56 m/sAs you can see, the swimmer slowed down over the second 200m.VelocityVelocity is somewhat quasi(prenominal) to speed but velocity involves both direction and speed. So, whereas speed is a scalar quantity, velocity is a vector quantity, that is, it has both magnitude and direction. Velocity also uses displacement as opposed to distance. Remember displacement is measured as the straight line distance an object travels from starting to ending position. Velocity is direction sensitive since it is dependent u pon displacement. Therefore, when you calculate velocity, you must also keep track of direction. Therefore, if you say an airplane has a velocity of 600 kmh, you would actually be a little vague. You should really say the airplane has a velocity of 600 kmh North. So, speed doesnt worry about direction, velocity does. Velocity is a positive number as we dont have cast out velocity. So to summarize, a airplane traveling at 600 kmh as a speed of 600 kmh. The self identical(prenominal) airplane has a velocity of 600 kmh, North. Finally, the same airplane probably had little acceleration in the middle of its trip as it would only drive positive acceleration and negative acceleration during take off and landing.Here is an interesting and challenging little riddle for you to cypher. Can you fill in the following table with acceleration, speed, and velocity selective information? We exist the following, the direction of travel is south and acceleration doubles every second. If youre f eeling confident you can also try and calculate the total distance that was covered over the 6 seconds. imply You can use the velocity for each second to help you.TimeVel.m/sAccel. m/s2*Speed.m/s0s1111s22s73s84s315s36s64AnswersTimeVel.m/sAccel. m/s2*Speed.m/s0s1111s321.52s743.53s1585.04s31167.755s633212.66s1276421.16*Average speed through with(predicate) that time periodSoAverage velocity = DisplacementTimeLet try some superfluous calculation examplesFor example, if an athlete runs around a 400 meter track in 50 seconds we can calculate numerous factors.What was the distance traveled?What was the displacement?What was the average speed?What was the average velocity?1. What was the distance traveled?Answer Easy nice = 400 meters2. What was the displacement?Answer Since the athlete ended up in the same place as they started, displacement is equal to zero.3. What was the average speed?Answer Speed = Distance/Time = 400 m/60 seconds = 6.66 m/sec4. What was the average velocity?Answe r Velocity = Displacement/Time = 0/60 seconds.In this case we end up with a value of zero and in this scenario average speed is a better indicator of overall performance.In legion(predicate) situations we actually calculate average velocity as speed because we cant gather the correct information to calculate speed. For example, if a punt returner catches the lubber on the 20 rate line and then avoids a few tackles to ultimately score a touchdown twelve seconds later, we assume the punt returner ran 80 yards. In fact, they may have run 100 yards with all the turning and weaving but we cant accurately calculate the true distance traveled and quite use displacement. For our purposes in sports, thats okay. You try the following problem.Review conundrumsCan you accurately calculate average speed, velocity, distance and displacement for each of the following situations? Hint You may not be able to calculate them all accurately.Problem1. A punt returner catches the lump on his own 40 yard line and scores a touchdown nine seconds later.2. A 100 meter sprinter runs the 100 meter in 10.0 seconds flat.AccelerationThe law of acceleration is Newtons second law and basically states The change of motion of an object is proportional to the string impressed and occurs in the direction in which the power is impressed.So far we have intercourseed about speed and velocity and performed some calculations. However, while speed and velocity are valuable components, they tend to provide us with drumhead information and very little about specific detail. For example, if we consider the data for a 200 meter race run in 20 seconds we know that average speed was 10 m/sec. However, we would not know any information about who accelerated the fastest or who was track after 100 meters. This information is also important as it helps with identifying speciality and weaknesses in athletes and in developing training programs for particular athletes. The measurement of acceleration is important. Acceleration is the rate of change in velocity. Therefore, when acceleration is zero, velocity is changeless. So when an object changes speed either by slowing up or down, or changes direction, it is accelerating (or decelerating). We can calculate acceleration by measuring the difference in velocity over the time it took for that change in velocity to occur. Consider this If you were to watch a 100M race the person leading at the 50M mark doesnt always win the race. The reason for this is that runners have different acceleration and deceleration rates, in other words their speed changes. Athletes vary dramatically in their acceleration. Some athletes are very fast over 40M but not over 100M and vice versa. SoAcceleration (a) = Velocity2 Velocity1 Where V2 is velocity at T2Tim Where V1 is velocity at T1Some measure you will see this presented as the change in velocity (Delta sign ) or the change in time (T)A = VTLook at the following acceleration example.Question A spr inter leaves the starting block at 2.5 m/s. wizard second later they are traveling at 5.5 m/s. What is the acceleration rate?Answer V2 V1 = 5.5 m/s 2.5 m/s = 3 m/s squaredT 1You will cable that we end up with meters per second squared as our answer would really be presented as 3 m/s/s.Heres another problem to try.Question A punt returner catches the addict standing still and begins to return. two seconds later his velocity was 5 m/s. What was his average acceleration over the first two seconds?Answer V2 V1 = 5 m/s 0 m/s = 3.5 m/s squaredT 2So far we have looked at relatively straightforward examples of speed, acceleration and velocity in that they have all been examples of horizontal movement. Now let us dishs the vertical components of projectile acceleration, speed and velocity.Factors Affecting AccelerationLinear acceleration is affected by many factors and you will generate from chapter ? that the messiness of an object is a very important one. Heavier objects acceler ate more slowly with a given force. This has to do with both inertia and mass. Heavier objects are harder to both accelerate and decelerate. Think about how easy it is to throw a basket lout versus a medicine thud. There are some other points to consider when looking at acceleration, speed, and velocity. First, we now know the units for velocity are meters per second (m/s) and meters per second squared for acceleration (m/s/s). For speed they are also m/s. Since acceleration (like velocity) is a vector quantity, it also has direction associated with it. The direction of acceleration depends on two factorsa. Whether the object is speeding up or slowing downb. Whether the object is moving in a negative (upwards) or positive (downward) directionWe can simplify this by saying that if an object is slowing down then its acceleration is in opposite direction of its motion. If it is speeding up then its acceleration is in the same direction as its motion.ThereforeAcceleration (m/s2) = mas s (kg)/force (newtons)Vertical speed, acceleration and velocityIf you were to throw a ball up in the air and then catch it again at the same height as you introduced it, how would the ending velocity be? Would it be greater, less, or the same as the release speed? If you guessed the same you would be correct. You see, all objects, whether traveling vertically or horizontally, are subjected to the unremitting force of gravity (9.81 m/s2). This means that as soon as the ball left field your hands it started to negatively (de)accelerate at 9.81 m/s2 until it had no more velocity. Then, it started to positively re-accelerate over the same distance (and time) at a rate of 9.81 m/s2 until you caught it again.This is a very neat relationship as it allows us to make many calculations based on this constant acceleration force. Projectiles are subjected to both vertical and horizontal components in their motion. The horizontal components are affected by the mass of the object and the accele ration force as previously mentioned. The vertical components are also affected by these two factors plus gravity. Consider this statement A ball shot horizontally (at zero degrees) has the same vertical component as a ball that is simply castped with no horizontal velocity. What this means is that if you were to throw a pass from your chest and it spud the aim 15 meters away 1.5 seconds later, and at the same time drop a second ball straight down from the same height, they would both hit the background signal at the exact same time. What this is showing us is that the force of gravity component is acting consistently regardless of whether the ball has a horizontal component or not. In other words adding a horizontal acceleration component does not affect in any way the force of gravity.Remember also that gravitational acceleration is a vector quantity comprising both magnitude and direction and acceleration is a squared variable to the magnitude of the force of gravity. This me ans that for every second an object is in free fall it will accelerate by ad additional 9.81m/s2. Thus the total distance traveled is directly proportional to the square of the time. Or we could say that if an object travels twice the time it will travel four times the distance. If an object travels for three seconds it will cover nine times the distance, for four seconds it is sixteen times the distance travelled in the first second. Look at the following.A coin is dropped from a cliff. The table shows how fast it is travelling at different time points.TimeSpeed m/s1 sec9.812sec19.623 sec29.434 sec39.245 sec49.056 sec58.867 sec96.23Consider this simple math problemQuestion A boy drops a ball from a balcony and records a time of 3 seconds for the ball to hit the ground. At what velocity did the ball hit the ground?Answer 29.43 m/sHow do we get this answer? Well, remember that gravity acts as a constant 9.81 m/s2. What this means is that for each second the ball is in career it acc elerates an additional 9.81 m/s. SoInsert schematic to demonstrateafter 1 second = 9.81 m/safter 2 seconds = 9.81 m/s + 9.81 m/s = 19.62 m/safter 3 seconds + 19.62 m/s + 9.81 m/s = 29.43 m/sThis is a simple illustration of the concept. Next oral sex, what velocity would the ball have to be released at ground height for the boy to catch it on the balcony?Answer A minimum of 29.43 m/s. The answer is the same because gravity and acceleration (or deceleration) is working(a) to the same effect when the ball is moving upwards. This is sometimes referred to a negative acceleration.Question.A boy is standing on a balcony and is curious about how high the balcony is from the ground. The boy drops a ball and records the time it takes to hit the ground. It took 3.2 seconds for the ball to hit the ground. The boy concludes that the balcony is 66.7m high.How did he work it out?Well at the end of the first second the ball was travelling 9.81m/s, at the end of the second the ball was travelling 19.62m/s, at the end of the third second the ball was travelling 29.43m/s. If you add these three distances together you get 58.86 meters travelled after three seconds. If the ball travelled another full second it would travel another 39.24m, but it only travelled in this order for 0.2 sec. So, 39.24m x 0.2sec =7.84m. Now we add the 58.86m + 7.84m = 66.7m, and thats our answer.There are some other factors to consider with vertical projectiles. The pattern of change in vertical velocity is symmetrical about the apex of the trajectory. So not only does the object land at the same speed it was released, it also follows the reverse flight path on the way down.Using these constant parameters we can now extend our calculations into more complex situations. For example, lets say you are watching a volleyball game in a high school gym with a 10 meter high ceiling. An opponent spikes the ball over the net and a player digs the ball at ground level at which time the ball has a velocity of 15 m/s. The question is will the ball hit the ceiling? To crystalise for this we can use an equation that combines several(prenominal) variables we talked about already.Where V2 = velocity at time 2V1 = velocity at time 1a = accelerationt = timeIn order to answer this question we need to look at what we know and what we want to know. Well, we want to know the distance (d) the ball travels. We already know a = 9.81 m/s2 and we know V1 = 15 m/s. We also know that at the apex the velocity is zero, so V2 can be set to zero. So now our normal looks like this1. 0 = V1 squared + 2ad2. 0 = (15 m/s) squared + 2 (-9.81 m/s squared) x dNow if we rearrange to solve for d our formula looks like= (19.62 m/s squared) x d = 225 m/s squared= d = 11.47 mThe answer is yes The ball will hit the ceiling as it will travel 11.47 m.Heres another similar problemA ball is deflected vertically at 18 m/s and the ceiling height is 11 meters. Will the ball hit the ceiling?Factors affecting projectile motionWe ha ve discussed several factors that affect the movement (or acceleration) of an object. The factors that affect vertical acceleration are the mass of the object, the force (speed) of release and gravity. Horizontal acceleration is affected only by mass and force of release (application). Gravity is of course a factor but not in determining its horizontal component. But sometimes we want to throw objects e.g. discus, hammer, etc. and while these projectiles are influenced by force and mass, there are other factors that influence how far the projectile will travel. We generally recognize three other factors that influence how far a projectile will travel when a constant force is use. They are1. Angle at which projectile is released.2. The speed of release.3. The height of release.The optimum tippytoe of release to increase horizontal displacement is 45. Projectiles released at over or below this cant will not reach their great distance. Look at control panel 1 to see how distance tr aveled varies with changing angles of release. You will see from table 1 that the optimum angle of release is 45 and after that the decrease in distance traveled is symmetrical as height compromises distance (I.e. follows the same pattern as increasing angle of release up to 45). The greater the speed of release the greater the distance a projectile will travel. This holds true simply because there is a greater acceleration force applied in the first place. Simply put, if you want to throw a ball further you need also to throw it harder. The greater the height of release the greater the distance a projectile will travel. If you consider field sports in athletics you will notice that most successful hammer, discus and javelin throwers are taller, giving the mechanical advantage over shorter competitors in that event. If you were to throw a ball from the top of a building it would strike the ground much further away than it would if you were to throw it from standing on the ground.Tab le 1 Distance a Projectile travels at a constant speed and height of release with change in angle of release. (need the reference)Speed of releaseRelease angleDistance Travelled10m/s103.49m10m/s206.55m10m/s308.83m10m/s4010.04m10m/s4510.19m10m/s501.04mIf you have watched a discuss contender or a hammer throw you might notice that these athletes are quite tall (often over 1.9m). The reason for this is that these athletes have an advantage over their shorter counterparts as their angle of release is already several centimeters higher.SummaryThis chapter has provided a basic introduction to the concepts of speed, acceleration and velocity. We have also looked at how differentiating between these variables is important and sometimes difficult. Using some known constants, such as the accelerating force of gravity (9.81 m/s2) allows us to calculate and even indicate the speeds, velocities and flight paths of selected projectiles. We have also discussed other factors that affect projectil e motion such as height and speed of release. While this information is very important, it is a basic introduction as there are many other more complex factors affecting speed, acceleration and velocity. We did not talk about shape or design or, indeed materials which also play a role in the way particular objects react to forces. The factors are extremely important but for now are beyond the cranial orbit of this text. Following this section are additional problems for you to solve and practice.Review ProblemsCan you provide a one sentence definition for each of the follow terms?DistanceDisplacementAccelerationVelocitySpeedPositionScalarVectorA ball rolls with an acceleration of -.5 m/s 2. If it stops after 7 seconds, what was its initial speed?A wheelchair long-distance runner has a speed of 5m/s after rolling down a small hill in 1.5sec. If the wheelchair underwent a constant acceleration of 3 m/s 2 during the descent, what was the marathoners speed at the top of the hill?A run ner completes 6.5 laps of a 400m track in 12 mins (720 secs). He starts half way around the bend. Can you calculate the following?a. Distance coveredb. Displacement after 12 minutesc. Runners average speedd. Runners average pace min/mile =A soccer ball is rolling across a field. At T = 0, the ball has an instantaneous velocity of 4 m/s. If acceleration occurs at a constant -0.3 m/s2 how long will it take to stop?A spank strikes a ground ball with an instantaneous velocity of 18m/s. If acceleration occurs at -0.7m/s2 how long will it take to stop?