Position Time Graphs
The variable on the x-axis
A radio signal takes 1.28 s to travel from a transmitter on the Moon to the surface of Earth. The radio waves travel at 3.00 x 108 m/s. What is the distance, in kilometers, from the Moon to Earth?
3.84 x 105 km
Find the uniform acceleration that causes a car’s velocity to change from 32 m/s to 96 m/s in an 8.0-s period
8 m/s2
A bag is dropped from a hovering helicopter. The bag is fallen for 2.0 s. What is the bag’s velocity?
20. m/s downward
An Indy car can complete 120 laps in 1.5 h. Even though the track is an oval rather than a circle, you can still find the average angular speed. Calculate the average angular speed of the Indy car.
0.14 rad/s
The variable on the y-axis.
What is position or velocity?
After 16.5 s, a jogger’s displacement is 200.0 m. What is the average velocity in km/h?
43.6 km/h
A car with a velocity of 22 m/s is accelerated uniformly at the rate of 1.6 m/s2 for 6.8 s. What is its final velocity?
33 m/s
A helicopter is rising at 5.0 m/s when a bag of its cargo is dropped. The bag falls for 2.0 s. What is the bag’s velocity?
-14.62 m/s
Or 14.62 m/s downward
The propellers, or screws, of a steamship push water away from the ship, causing the ship to move forward. Suppose a ship’s screw turns 106 rad clockwise in 7.5 s. What is the average angular speed of the screw? (Clockwise is the negative direction)
-14.1 rad/s
What does a velocity time graph of an object with constant velocity look like?
horizontal line
A “moving sidewalk” in a busy airport terminal moves 1.0 m/s and is 200.0 m long. A passenger steps onto one end and walks, in the same direction as the sidewalk is moving, at a rate of 2.0 m/s relative to the moving sidewalk. How much time does it take the passenger to reach the opposite end of the walkway?
67 s
Determine the final velocity of a proton that has an initial velocity of 2.35 x 105 m/s and then is accelerated uniformly in an electric field at the rate of -1.00 x 1012 m/s2 for 1.5 x 10-7 s.
8.5 x 104 m/s
When it is completed in 2002, the International Financial Center in Taipei, Taiwan, will be the tallest building in the world. Suppose a construction worker on the top-most floor of the building accidentally knocks a wrench off a ledge. The wrench hits the ground below 9.56 s later. What is the distance between the top-floor of the International Financial Center and the ground. Assume there is no air resistance.
448 m
A barrel is given a downhill rolling start of 1.5 rad/s at the top of a hill. Assume a constant angular acceleration of 2.9 rad/s2. If the barrel takes 11.5 s to get to the bottom of the hill, what is the final angular speed of the barrel?
35 rad/s
What does the slope of a linear position-time graph represent?
The velocity
Laura is skydiving when at a certain altitude she opens her parachute and drifts toward the ground with a constant velocity of 6.50 m/s, straight down. What is Laura’s displacement if it takes her 34.0 s to reach the ground?
221 m downward
A race car can be slowed with a constant acceleration of -11.0 m/s2. If the car is going 55.0 m/s, how many meters will it travel before it stops?
138 m
A physics student throws a softball straight up into the air with a speed of 17.5 m/s. The ball is in the air for a total of 3.60 s before it is caught at its original position. How high does the ball rise?
15.8 m
A barrel is given a downhill rolling start of 1.5 rad/s at the top of a hill. Assume a constant angular acceleration of 2.9 rad/s2. What angular displacement does the barrel experience during the 11.5 s ride?
210 rad
What would a velocity-time graph look like of an object at rest?
horizontal line at 0
An antelope can run 90.0 km/h. A cheetah can run 117 km/h for short distances. The cheetah, however, can maintain this speed only for 30.0 s before giving up the chase. Can an antelope with a 150.0 m lead outrun a cheetah?
No, the cheetah can run 225 m farther than the antelope in 30.0 s, so a 150.0 m lead is not sufficient
Engineers are developing new types of guns that might someday be used to launch satellites as if they were bullets. One such gun can give a small object a velocity of 3.5 km/s while moving it through a distance of only 2.0 cm. What acceleration does the gun give this object?
3.06 x 108 m/s2
You drop a ball from a height of 2.0 m. It falls to the floor, bounces straight upward 1.3 m, falls to the floor again, and bounces 0.7 m. At the top of the second bounce, what is the total distance that the ball has traveled?
5.3 m
The only circular border in the United States is between northern Delaware and Pennsylvania. The border has a length of about 35.0 km. If a vehicle traveling through an arc length of this size has an angular displacement with a magnitude of 1.75 rad, what is the border’s radius?
20.0 km