# Constant Acceleration: A Special Case

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**Constant Acceleration: A Special Case**

22E. An automobile driver increases the speed at a constant rate from 25 km/h to 55 km/h in 0.50 min. A bicycle rider speeds up at a constant rate from rest to 30 km/h in 0.50 min. Calculate their accelerations.

23E. A muon (an elementary particle) enters a region with a speed of 5.00 x 106 m/s and then is slowed at the rate of 1.25 x 1014 m/s2. (a) How far does the muon take to stop? (b) Graph x versus I and I’ versus I for the muon.

24E. The head of a rattlesnake can accelerate at 50 m/s2 in striking a victim. If a car could do as well. how long would it take to reach a speed of 100 km/h from rest 25E. An electron has a constant acceleration of +3.2 m/s2. At certain instant its velocity is +9.6 m/s. What is its velocity (a) 2.5 earlier and (b) 2.5 s later?

26E. The speed of a bullet is measured to be 640 m/s as the bullet emerges from a barrel of length 1.20 m. Assuming constant acceleration, find the time that the bullet spends in the barrel after it is fired.

27E. Suppose a rocket ship in deep space moves with constant acceleration equal to 9.8 m/s2. which gives the illusion of normal gravity during the flight. (a) If it starts from rest. how long will it take to acquire a speed one-tenth that of light. which travels at 3.0 X 108 m/s? (b) How far will it travel in so doing?

28E. A jumbo jet must reach a speed of 360 km/h on the runway for takeoff. What is the least constant acceleration needed for takeoff from a 1.80 km runway?

29E. An electron with initial velocity enters a region 1.0 em long where it is electrically accelerated . It emerges with velocity. What is its acceleration. assumed constant?(Such a process occurs in conventional television sets.).

3OE. A world’ s land speed record was set by Colonel John P. Stapp when in March 1954 he rode a rocket-propelled sled that moved along a track at 1020 km/h. He and the sled were brought to a stop in 1.4 s. In g units, what acceleration did he experience while stopping?

3lE. The brakes on your automobile are capable of creating a deceleration

of 5.2 m/s2. (a) If you are going 137 km/h and suddenly see a state trooper. what is the minimum time in which you can get your car under the 90 km/h speed limit? (The answer reveals the futility of braking to keep your high speed from being detected with a radar or laser gun.) (b) Graph x versus I and v versus I for such a deceleration.

32E. Figure 2-21 depicts the motion of a particle moving along an x axis with a constant acceleration. What are the magnitude and direction of the particle’S acceleration?

3SP. A car traveling 56.0 km/h is 24.0 m from a barrier when the 0 t (s)

driver slams on the brakes. The car hits the barrier 2.00 s later. (a) What is the car’s constant deceleration before impact? (b) How fast is the car traveling at impact?

34P. A red train traveling at 72 km/h and a green train traveling at 144 km/h are headed toward one another along a straight, level track. When they are 950 m apart, each engineer sees the other’s train and applies the brakes. The brakes decelerate each train at the rate . Is there a collision? If so, what is the speed of each train at impact? If not, what is the separation between the trains when they stop?

35P. A car moving with constant acceleration covered the distance between two points 60.0 m apart in 6.00 s. Its speed as it passes the second point was 15.0 m/s. (a) What was the speed at the first point? (b) What was the acceleration? (c) At what prior distance from the first point was the car at rest? (d) Graph x versus I and v versus t for the car from rest.

36P. At the instant the traffic light turns green, ‘an automobile starts with a constant acceleration a of 2.2 m/s. At the same instant a truck, traveling with a constant ‘speed pf 9.5 mins, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the car be traveling at that instant?

37P. To stop a car, first you require a certain reaction time to begin

braking; then the car slows under the constant braking deceleration.

Suppose that the total distance moved by your car during these two

phases is 56.7 m when its initial speed is 80.5 km/h, and 24.4 m

when its initial speed is 48.3 km/h. What are (a) your reaction time

and (b) the magnitude of the deceleration?

38P. When a high-speed passenger train traveling at 161 km/h rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance D = 676 m ahead . The locomotive is moving at 29.0

km/h. The engineer of the high-speed train immediately applies the brakes. (a) What must be the magnitude of the resulting constant deceleration if a collision is to be just avoided? (b) Assume that the engineer is at x = 0 when, at t = 0, he first spots the locomotive. Sketch the curves representing the locomotive and high-speed train for the situations in which a collision is just avoided and is not quite avoided.

39P. An elevator cab in the New York Marquis Marrion has a total run of 190 m. Its maximum speed is 305 m min. Its acceleration and deceleration both have a magnitude of 1.22 m s. (a) How far does the cab move while accelerating to full speed from rest? (b) How long does it take to make the nonstop 190 m run, starting and ending at rest?