2. 1D Motion / Kinematics

A moving hockey puck encounters a patch of rough ice and slides 90cm before coming to a full stop. Assuming a constant deceleration of 8 m/s², what was the puck's initial speed?

Certain rifles can fire a bullet with a speed of 970 m/s just as it leaves the muzzle (this speed is called the muzzle velocity). The muzzle is 70.0 cm long and the bullet is accelerated uniformly from rest within it. 

For how long (in ms) is the bullet in the muzzle?

A car accelerates from 5 m/s to 21 m/s at a constant 3.0 m/s². How far does it travel while accelerating?

(II) A baseball pitcher throws a baseball with a speed of 43 m/s. Estimate the average acceleration of the ball during the throwing motion. In throwing the baseball, the pitcher accelerates it through a displacement of about 3.5 m, from behind the body to the point where it is released (Fig. 2–44).

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(II) A car traveling 85 km/h slows down at a constant 0.50 m/s² just by 'letting up on the gas.' Calculate

(c) the distance it travels during the first and fifth seconds.

A package of mass m is placed onto a horizontal conveyor belt moving at speed v (Fig. 7–32). The coefficient of kinetic friction between package and belt is μₖ . <IMAGE>

(b) What is the package's displacement d during this time?

(II) An 85-m-long train begins uniform acceleration from rest. The front of the train has a speed of 18 m/s when it passes a railway worker who is standing 180 m from where the front of the train started. What will be the speed of the last car as it passes the worker? (See Fig. 2–45.) <IMAGE>

A person who is properly restrained by an over-the-shoulder seat belt has a good chance of surviving a car collision if the deceleration does not exceed 30 'g's' (1.00 g = 9.80 m/s². Assuming uniform deceleration at 30 g's, calculate the distance over which the front end of the car must be designed to collapse if a crash brings the car to rest from 95 km/h.

A robot used in a pharmacy picks up a medicine bottle at t = 0. It accelerates at 0.20 m/s² for 4.5 s, then travels without acceleration for 68 s and finally decelerates at ―0.40 m/s² for 2.5 s to reach the counter where the pharmacist will take the medicine from the robot. From how far away did the robot fetch the medicine?

Determine the stopping distances for an automobile going a constant initial speed of 95 km/h in the +𝓍 direction, and human reaction time of 0.40 s:

(a) for an acceleration a = ― 2.5 m/s²"

(I) A car slows down from 28 m/s to rest in 6.3 s. What was its (constant) acceleration?

A world-class sprinter can reach a top speed (of about 11.5 m/s) in the first 18.0 m of a race. What is the average acceleration of this sprinter and how long does it take her to reach that speed?

"Consider the street pattern shown in Fig. 2–51. Each intersection has a traffic signal, and the speed limit is 40 km/h. Suppose you are driving from the west at the speed limit. When you are 10.0 m from the first intersection, all the lights turn green. The lights are green for 13.0 s each.                                                                                                                          

(b) Another car was stopped at the first light when all the lights turned green. It can accelerate at the rate of 2.00 m/s² to the speed limit. Can the second car make it through all three lights without stopping? By how many seconds would it make it, or not make it?                                                                                                                                       

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Show that v = (v + v₀)/2 (see Eq. 2–12d) is not valid when the acceleration a = A + Bt, where A and B are non-zero constants.