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Physics problems: kinematics

Motion with constant acceleration

 

Problem 2.

Is it possible that the car could have accelerated to 55mph within 268 meters if the car can only accelerate from 0 to 60 mph in 15 seconds?

Solution

 

Problem 7.

A car is accelerating at .  Find its acceleration in .

Solution

 

Problem 9.

An airliner reaches its takeoff speed of 163 mph in 36.2 s. What is the magnitude of its average acceleration.

Solution

 

Problem 10.

A car is initially traveling due north at 23 m/s.
(a) Find the velocity of the car after 4 s if its acceleration is due north.
(b) Find the velocity of the car after 4 s if its acceleration is instead due south.

Solution

 

Problem 12.

You are driving along the street at the speed limit (35mph) and 50 meters before reaching a traffic light you notice it becoming yellow. You accelerate to make the traffic light within the 3 seconds it takes for it to turn red. What is your speed as you cross the intersection? Assume that the acceleration is constant and that there is no air resistance.

Solution

 

Problem 19.

A speedboat increases its speed uniformly from 20 m/s to 30 m/s in a distance of 200m. Find

(a) the magnitude of its acceleration and

(b) the time it takes the boat to travel the 200-m distance.

Solution

 

 

 

 

Problem 21.

An aircraft has a lift-off of 120km/h.

(a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 240m?

(b) How long does it take the aircraft to become airborne?

Solution

 

Problem 33.

A rocket is fired vertically upwards with initial velocity 80 m/s at the ground level. Its engines then fire and it is accelerated at until it reaches an altitude of 1000 m. At that point the engines fail and the rocket goes into free-fall. Disregard air resistance.

(a)  How long was the rocket above the ground?

(b)  What is the maximum altitude?

(c) What is the velocity just before it collides with the ground?

Solution

 

Problem 37.

A displacement, s, of an object as a function of time, t, is given by

a) Find an expression for the acceleration of the object

b) Explain why this expression indicates that the acceleration is not constant

Solution

 

Problem 41.

A motor scooter travels east at a speed of 13 m/s. The driver then reverses direction and heads west at 17 m/s.  What was the change in velocity of the scooter?

Solution

 

Problem 53.

A car starts from the rest and accelerates uniformly for t=5 seconds over a distance of 100m. Find the acceleration of the car.

Solution

 

Problem 54.

On the moon, an object is dropped from a height of 2 m. The acceleration of gravity on the moon is . Determine the time it takes for the object to fall to the surface of the moon.

Solution

 

 

 

 

Problem 58.

You are driving towards a traffic signal when it turns yellow. Your speed is 55 km/h, and your best deceleration has the magnitude of . Your best reaction time before breaking is . To avoid having the front of your car enter the intersection after the light turns red, should you break to a stop or continue to move at 55 km/h if the distance to the intersection and the duration of the yellow light are

(a) 40m and 2.8s, and

(b) 32m and 1.8s?

Solution

 

Problem 65.

A skier is accelerating down a 30 degree hill at .

(a) What is the vertical component of her acceleration?

(b) How long will it take her to reach the bottom of the hill, assuming she starts from rest and accelerates uniformly, if the elevation is 300 m?

Solution

 

Problem 68.

The acceleration of an object as a function of time is . Determine the

(a) velocity and

(b) the position of the object as a function of time

if it is located at x = 2 m and has a velocity of 3 m/s at time t = 0 s.

Solution

 

Problem 74.

A car going at 10 m/s undergoes an acceleration of for 6 seconds.  How far did it go when it was accelerating?

Solution

 

Problem 75.

What is the displacement of a car accelerating from 5 m/s (right) to 10 m/s (right) in 2.0s?

Solution

 

Problem 78.

A man is driving at the speed 40 mph when he see an obstacle at distance 300 ft ahead of his position. The driver applies the brakes and decelerates at How long does it take him to stop the vehicle? How far from the obstacle will the driver be when he finally stops?

Solution

 

 

 

 

Problem 89.

A toy rocket is launched with an initial velocity of 12.0 m/s in the horizontal direction from the roof of a 37.0 m -tall building. The rocket's engine produces a horizontal acceleration of , in the same direction as the initial velocity, but in the vertical direction the acceleration is , downward.  Air resistance can be neglected. How long is the rocket in the air before it hits the ground?

Solution

 

Problem 90.

A toy rocket is launched with an initial velocity of 12.0 m/s in the horizontal direction from the roof of a 37.0 m -tall building. The rocket's engine produces a horizontal acceleration of , in the same direction as the initial velocity, but in the vertical direction the acceleration is , downward.  Air resistance can be neglected. How far does the rocket travel in horizontal direction before it hits the ground?

Solution

 

Problem 92.

A car is moving with a velocity of 72 km/h. It's velocity is reduced to 36 km/h after  covering a distance of 200 m. Calculate its acceleration.

Solution

 

Problem 93.

A car initially at rest, starts moving with a constant acceleration of  and travels a distance of 25 m. Calculate its final velocity.

Solution

 

Problem 97.

An astronaut jumps from an airplane. After he had fallen 40 m, then his parachute opens. Now he falls with a retardation of  and reaches the earth with a velocity of 3.0 m/s. What was the height of the aeroplane?

Solution

 

 

 

 

 

Problem 99.

Albert is riding his scooter at a velocity of 80 km/h when he sees an old woman crossing the road 45 m away he immediately steps hard on the break to get the maximum deceleration of . How far will he go before stopping, will he hit the old woman?

Solution

 

Problem 101.

A particle is moving eastwards with a velocity 5 m/s, changes its direction northwards in 10 seconds and moves with the same magnitude of velocity.  Find the average acceleration of the particle.

Solution

 

Problem 102.

A car traveling at a constant speed of 30 m/s passes a highway patrol car, which is at rest. The police officer accelerates at a constant rate of  and maintains this rate of acceleration until he pulls next to the speeding car. Assume that the police car starts to move at the moment the speeder passes the police car. What is the time requires for the police officer to catch the speeder?

Solution

 

Problem 53 (dynamics).

A block of mass 13.6 kg is sliding at an initial velocity of 4.65 m/s along horizontal surface to the right. The surface has a coefficient of kinetic friction of 0.254. How far will it slide before coming to rest?

Solution

 

Problem 114.

An object has an initial speed of 8.0 m/s and is stopped in intervals of 0.20 s. What is the magnitude and direction of his acceleration.

Solution

 

Problem 116.

A car was traveling at 12m/s when the driver stepped on the brakes. If the car comes to a full stop in 5.0 s, what was its acceleration? What distance did it cover?

Solution

 

Problem 117.

Brakes applied to a car produce a uniform retardation of acceleration. If the car was travelling with a velocity of 27 m/s, what distance will it cover before coming to rest?

Solution

 

 

 

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