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?

Starting from rest, a car accelerated to

20 m / s

4 s

. How far did the car travel as it sped up? Assume constant acceleration.

197

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?

114

rank

A speed skater moving to the left across frictionless ice at 8.0 m/s hits a 5.0-m-wide patch of rough ice. She slows steadily, then continues on at 6.0 m/s. What is her acceleration on the rough ice?

558

a. Find an expression for the minimum stopping distance dₛₜₒₚ of a car traveling at speed v₀ if the driver's reaction time is Tᵣₑₐ꜀ₜ and the magnitude of the acceleration during maximum braking is a constant a₆ᵣₐₖₑ.

347

A car starts from rest at a stop sign. It accelerates at 4.0 m/s² for 6.0 s, coasts for 2.0 s, and then slows down at a rate of 3.0 m/s² for the next stop sign. How far apart are the stop signs?

970

You're driving down the highway late one night at 20 m/s when a deer steps onto the road 35 m in front of you. Your reaction time before stepping on the brakes is 0.50 s, and the maximum deceleration of your car is 10 m/s². a. How much distance is between you and the deer when you come to a stop?

1730

A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the magnitude of the jet's acceleration, assuming it to be a constant acceleration?

541

A sprinter can accelerate with constant acceleration for 4.0 s before reaching top speed. He can run the 100 meter dash in 10.0 s. What is his speed as he crosses the finish line?

478

A motorist is driving at 20 m/s when she sees that a traffic light 200 m ahead has just turned red. She knows that this light stays red for 15 s, and she wants to reach the light just as it turns green again. It takes her 1.0 s to step on the brakes and begin slowing. What is her speed as she reaches the light at the instant it turns green?

425

At launch a rocket ship weighs 4.5 million pounds. When it is launched from rest, it takes 8.00 s to reach 161 km/h; at the end of the first 1.00 min, its speed is 1610 km/h. (a) What is the average acceleration (in m/s2) of the rocket (i) during the first 8.00 s and (ii) between 8.00 s and the end of the first 1.00 min?

465

An astronaut has left the International Space Station to test a new space scooter. Her partner measures the following velocity changes, each taking place in a 10-s interval. What are the magnitude, the algebraic sign, and the direction of the average acceleration in each interval? Assume that the positive direction is to the right. (a) At the beginning of the interval, the astronaut is moving toward the right along the x-axis at 15.0 m/s, and at the end of the interval she is moving toward the right at 5.0 m/s. (b) At the beginning she is moving toward the left at 5.0 m/s, and at the end she is moving toward the left at 15.0 m/s. (c) At the beginning she is moving toward the right at 15.0 m/s, and at the end she is moving toward the left at 15.0 m/s.

451

A pilot who accelerates at more than 4g begins to 'gray out' but doesn't completely lose consciousness. (b) How far would the plane travel during this period of acceleration? (Use 331 m/s for the speed of sound in cold air.)

566

A pilot who accelerates at more than 4g begins to 'gray out' but doesn't completely lose consciousness. (a) Assuming constant acceleration, what is the shortest time that a jet pilot starting from rest can take to reach Mach 4 (four times the speed of sound) without graying out? (Use 331 m/s for the speed of sound in cold air.)

495

In the fastest measured tennis serve, the ball left the racquet at 73.14 m/s. A served tennis ball is typically in contact with the racquet for 30.0 ms and starts from rest. Assume constant acceleration. (a) What was the ball's acceleration during this serve?

1244

A Fast Pitch. The fastest measured pitched baseball left the pitcher's hand at a speed of 45.0 m/s. If the pitcher was in contact with the ball over a distance of 1.50 m and produced constant acceleration, (a) what acceleration did he give the ball?

1149

An antelope moving with constant acceleration covers the distance between two points 70.0 m apart in 6.00 s. Its speed as it passes the second point is 15.0 m/s. What is (b) its acceleration?

1214

The human body can survive an acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than 250 m/s2. If you are in an automobile accident with an initial speed of 105 km/h(65 mi/h) and are stopped by an airbag that inflates from the dashboard, over what distance must the airbag stop you for you to survive the crash?

1782

When you sneeze, the air in your lungs accelerates from rest to 150 km/h in approximately 0.50 s. What is the magnitude of the acceleration of the air in m/s^2

176

How far has the car traveled when it reaches 60 mph? Give your answer both in SI units and in feet.

108

You are driving to the grocery store at 20 m/s. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.50 s and that your car brakes with constant acceleration. What magnitude braking acceleration will bring you to a stop exactly at the intersection?

129

What constant acceleration, in SI units, must a car have to go from zero to 60 mph in 10 s?

111

For an object starting from rest and accelerating with constant acceleration, distance traveled is proportional to the square of the time. If an object travels 2.0 furlongs in the first 2.0 s, how far will it travel in the first 4.0 s?

546

You throw a 5.5 g coin straight down at 4.0 m/s from a 35-m-high bridge. (b) What is the speed of the coin just as it hits the water?

143

(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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108

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

156

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?

337

(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>

122

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.

140

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?

112

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.