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Practice with Motion Equations and Motion Graphs:

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If the problem requires acceleration due to gravity, use the value 9.8 m/s2.

Constant Velocity

An airplane travels from Calgary to Toronto in 4 h 20 min. Find the average speed if the distance between the two cities is 4330 km.

An earthquake created a succession of giant water waves, called tsunamis, off the coast of Japan. The waves traveled at an average velocity of 800. km/h. If the distance from the source of the quake to the northern coast of Australia was 8.20 103 km, how long did it take the first wave to reach the Australian coast?

A train travels 58 km at an average velocity of 77 km/h [E], waits for 5.0 min at a station, and then runs for half an hour at an average velocity of 64 km/h [E]. Find:

the total displacement of the train, and

the average velocity for the whole trip.

Constant Acceleration

An electric train initially moving at 25 km/h accelerates to 35 km/h in 20 s. Find its average acceleration in m/s2.

A rocket ship in space moves with a constant acceleration of 9.8 m/s2. If it starts from rest, how long will it take to reach a velocity one-tenth that of light (vlight = 3.00 x 108 m/s)?

A plane traveling at 200 km/h [N] accelerates at the rate of 5.0 km/h/s [N] for 1.0 min. What is its final velocity?

A train traveling at 100 km/h slows down with a uniform deceleration of 0.60 m/s2. How long does it take to stop?

A motorist traveling at 90 km/h applies his brakes and comes to rest with uniform deceleration in 20 s. Calculate the acceleration in m/s2.

A bullet is fired straight up with an initial velocity of 460 m/s. How long will it take it to reach its highest point and how high will that be? (The air resistance may be neglected.)

A stone is thrown straight down from the top of a cliff with an initial velocity of 6.0 m/s. It reaches the bottom in 3.0 s. How high is the cliff?

With what speed must a ball be thrown vertically upward in order to rise to a height of 16 m? How long will that same ball take to rise 16 m?

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Graphing Techniques

Using the graph below of the motion of a car traveling in a straight line, determine each of the following.

the velocity of the car in each of the intervals

the average velocity of the car for the whole trip.

For the graph to the right,

Which sections of this graph represent:

uniform velocity,

the object at rest, and

acceleration

What is the average velocity in the intervals:

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t = 0 s to t = 5.0 s, and

t = 15 s to t = 20 s?

What is the instantaneous velocity at:

t = 3.0 s,

t = 24 s, and

t = 8.0 s

The v-t graph to the right represents the motion of a car. Assume that the positive direction is North.

In which interval(s) is the velocity uniform?

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In which interval(s) is the acceleration uniform?

How far has the car travelled after 11 s and after 25 s?

How far did the car travel in the 13th second?

What is the acceleration:

in the first 5.0 s and

from t = 11 s to t = 14 s?

What is the instantaneous acceleration at t = 12.5 s and t = 22 s?

A car accelerates uniformly from rest at the rate of 2.0 m/s2 for 6.0 s. It then maintains a constant velocity for 0.50 min. Finally, the brakes are applied, and the vehicle slows down at a uniform rate and comes to rest in 5.0 s. Find:

the maximum velocity of the car, and

the total displacement.

At right is the v-t graph for the previous problem. Find the total displacement, using graphing techniques.

A ball rolls along the floor, up a sloping board, and then back down the board and across the floor again. The graph below represents this motion.

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At what time is the ball at its highest point?

What was the acceleration when the ball was

rolling up the board,

rolling down the board, and

at rest at the top point?

How far up the board did the ball go?

What was the total displacement of the ball over the 9.0 s trip?

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The graph to the right describes the motion of a capsule carried on a rocket fired vertically upward. The rocket ejected the capsule at its highest point. The capsule fell freely with the rocket until its parachute opened at t = 300 s.

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At what time did the rocket reach its highest altitude?

What was the maximum altitude of the rocket?

What was the acceleration of the rocket during

the first stage, and

the second stage

What was the average acceleration of the capsule during the interval

t = 100 s to t = 300 s?

What was happening during the period t = 300 s to t = 400 s?

What was the terminal velocity of the capsule just before splashdown?

More Challenging Questions

An executive jet cruises at 700 km/h. If the winds are light, it consumes kerosene at the rate of 38.0 L/min. If the jet's fuel tanks contain 6840 L when full, what is its maximum range? Look at units!

A British Concorde (BC) and a French Concorde (FC) flew in opposite directions around the world, a distance of 40 000 km. The BC covered half of its flight distance at a supersonic speed of 2500 km/h and the other half at a subsonic speed of 1000 km/h. The FC spent half of its flight time at 2500 km/h and the other half at 1000 km/h. Which Concorde completed the trip first, and by how many hours did it beat the other? (SIN '76)

The Easter bunny runs along a straight and narrow path with a constant speed of 25 m/s. He passes a sleeping tortoise, which immediately starts to chase the bunny with a constant acceleration of 3.0 x 10-3 m/s2. How long does it take the tortoise to catch the bunny? (Answer in hours.) (SIN '80)

At the instant when the traffic light turns green, an automobile starts with a constant acceleration of 1.8 m/s2. At the same instant a truck traveling with a constant speed of 8.5 m/s overtakes and passes the automobile.

How far beyond the starting point will the automobile overtake the truck?

How fast will the car be traveling at that instant?

A turtle is moving with a constant acceleration along a straight ditch. He starts his stopwatch as he passes a fence post and notes that it takes him 10 s to reach a pine tree 10 m farther along the ditch. As he passes the pine tree, his speed is 1.2 m/s. How far was he from the fence post when he started from rest? (SIN '76)

Two trains, one traveling at 100 km/h and the other at 128 km/h, are headed towards one another along a straight, level track. When the trains are 1.2 km apart, each engineer simultaneously sees the other's train and applies the brakes. Both trains have equal, constant decelerations 0.9 m/s2. Will there be a collision?

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