Linear Motion

Problems for solution without assistance

Problem 1

From Pillar to Post. Starting from a pillar, you run 200 m east(the +x-direction) at an average speed of 4.0 m/s, then run 280 m west at an average speed of 7.0 m/s to a post. Calculate your a) average speed from pillar to post; b) average velocity from pillar to post.

Problem 2

A physics professor leaves her house and walks along the sidewalk toward campus. After 5 min it starts to rain, and she returns home. Her distance from her house as a function of time is shown in the Figure 1. At which of the labeled points is her velocity:
a) zero?
b) constant and positive?
c) constant and negative?
d) increasing in magnitude?
e) decreasing in magnitude?

Figure 1.

Problem 3

A car is stopped at a trafic light. It then travels along a straight road so that its distance from the light is given by x = bt² + ct³, where b = 1.40m/s² and c = 0.150m/s³.
a) Calculate the average velocity of the car for the time interval t =0 to t =10.0 s.
b) Calculate the instantaneous velocity of the car at I) t =0; II) t =5.0 s; III) t =10.0 s.

Problem 4

An astronaut has left Spacelab V to test a new space scooter for possible use in constructing Space Habitat I. Her partner measures the following velocity changes, each taking place in a l0-s interval. What are the magnitude, the algebraic sign, and the direction of the average acceleration in each interval described below? Assume that the positive direction is to the right.
a) At the beginning of the interval the astronaut is moving to the right along the x-axis at 20.0 m/s, and at the end of the interval she is moving to the right at 5.0 m/s.
b) At the beginning she is moving to the left at 5.0 m/s, and at the end she is moving to the left at 20.0 m/s.
c) At the beginning she is moving to the right at 20.0 m/s, and at the end she is moving to the left at 20.0 m/s.

Problem 5

The human body can survive a negative acceleration trauma incident (sudden stop) if the magnitude of the acceleration is less than 250 m/s2 (approximatly 25 g). If you are in an automobile accident with an initial speed of 88 km/h (55 mi/h) and are stopped by an airbag that in°ates from the dashboard, over what distance must the airbag stop if you are to survive the crash?

Problem 6

An antelope moving with constant acceleration covers a distance between two points that are 80 m apart in 7.00 s. Its speed as it passes the second point is 15.0 m/s.
a) What is speed at the first point?
b) What is the acceleration?

Problem 7

The catapult of the aircraft carrier USS Abraham Lincoln accelerates an F/A-18 Hornet jet fighter from rest to takeof speed of 173 mi/h in a distance of 307 ft. Assume constanl acceleration.
a) Calculate the acceleration of the fighter in m/s
b) Calculate the time required for the fighter to be accelerated to takeof speed.

Problem 8

A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. The driver sees a small gap between a care, and an eighteen-wheel truck and accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has speed 25 m/s (55 mi/hr) when it reaches the end of the 120-m long ramp.
a) What is the acceleration of the car?
b) How much time does it take the car to travel the length of the ramp?
c) The tra±c on the freeway is moving at a constant speed of 25 m/s. What distance does the tra±c travel while the car is moving the length of the ramp?

Problem 9

An airplane travels 420 m down the runway before takeoff. It starts from rest, moves with constant acceleration, it becomes airborne in 16.0 s. What is its speed, in m/s, when it takes off?

Problem 10

At time t =0 a Corvette is traveling on a long, straight stretch of highway in Arizona at a constant speed of 25 m/s. This motion continues for 20 s. Then the driver, worried that she is behind schedule, accelerates at a constant rate for 5 s to bring the car's speed to 35 m/s. The car travels at this new speed for 10 s. But then the driver spots a police motorcycle parked behind a large cactus up ahead, and slows with a constant acceleration of magnitude 4.0 m/s² until the car's speed is reduced once again to the legal limit of 25 m/s. She then maintains this speed and waves to the officer as she passes him 5 s later.
a) For the motion of the car from t =0 until when the car passes the parked motorcycle, draw accurate a - t, v - t, and x - t graphs.
b) Draw a motion diagram showing the position, velocity,and acceleration of the car.

Problem 11

A spaceship ferrying workers to Moon Base I takes a straight-line path from the earth to the moon, a distance of about 400,000 mm. Suppose it accelerates at 20.0 m/s² for the first 10.0 min of the trip, then travels at constant speed until the last 10.0 min, when it accelerates at -20.0 m/s², just coming to rest as it reaches the moon.
a) What is the maximum speed attained?
b) What fraction of the total distance is traveled at constant speed?
c) What total time is required for the trip?

Examples of solutions

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