Kinematics: Velocity, Acceleration, and Motion Graphs
Interpreting motion with equations, graphs, and units
Kinematics: Velocity, Acceleration, and Motion Graphs
Interpreting motion with equations, graphs, and units
Physics - Grade 9-12
- 1
A car travels 120 meters east in 10 seconds. What is its average velocity?
Use average velocity = displacement / time.
The average velocity is 12 meters per second east because velocity equals displacement divided by time, so 120 m divided by 10 s equals 12 m/s east. - 2
A cyclist speeds up from 4 meters per second to 10 meters per second in 3 seconds. What is the cyclist's average acceleration?
The average acceleration is 2 meters per second squared because acceleration equals change in velocity divided by time, and (10 - 4) / 3 = 2 m/s^2. - 3
A runner moves with a constant velocity of 6 meters per second for 8 seconds. How far does the runner travel?
For constant velocity, displacement = velocity x time.
The runner travels 48 meters because distance equals velocity times time, so 6 m/s multiplied by 8 s equals 48 m. - 4
An object has an initial velocity of 5 meters per second and accelerates at 2 meters per second squared for 4 seconds. What is its final velocity?
The final velocity is 13 meters per second because final velocity equals initial velocity plus acceleration times time, so 5 + (2 x 4) = 13 m/s. - 5
A ball rolling along the floor slows from 9 meters per second to 3 meters per second in 2 seconds. What is its average acceleration?
A decrease in velocity gives a negative acceleration if the positive direction stays the same.
The average acceleration is -3 meters per second squared because acceleration equals change in velocity divided by time, and (3 - 9) / 2 = -3 m/s^2. The negative sign shows the ball is slowing down in the chosen positive direction. - 6
On a position-time graph, a line rises steadily from left to right with a constant slope. What does this tell you about the object's motion?
This tells you the object is moving with a constant positive velocity. A straight line on a position-time graph means the velocity is constant, and a positive slope means position is increasing over time. - 7
On a position-time graph, a horizontal line is shown from 2 seconds to 6 seconds. What does this mean about the object's motion during that time interval?
Slope on a position-time graph represents velocity.
This means the object is at rest during that interval. A horizontal line on a position-time graph shows that position is not changing, so the velocity is zero. - 8
On a velocity-time graph, the velocity increases from 2 meters per second at 0 seconds to 8 meters per second at 3 seconds. What is the acceleration?
The acceleration is 2 meters per second squared because the slope of a velocity-time graph equals acceleration, and (8 - 2) / 3 = 2 m/s^2. - 9
On a velocity-time graph, a line stays at -4 meters per second for 5 seconds. What does this tell you about the object's motion?
A horizontal line on a velocity-time graph means the velocity is not changing.
This tells you the object is moving with a constant velocity of -4 meters per second for the entire 5 seconds. The negative sign shows the motion is in the negative direction, and the horizontal line shows zero acceleration. - 10
A train moving at 20 meters per second comes to rest in 5 seconds. What is its average acceleration?
The average acceleration is -4 meters per second squared because acceleration equals change in velocity divided by time, and (0 - 20) / 5 = -4 m/s^2. - 11
A student walks 30 meters east in 10 seconds, then 10 meters west in 5 seconds. What is the student's average velocity for the whole trip?
Average velocity uses total displacement, not total distance.
The student's average velocity is about 1.33 meters per second east because the total displacement is 20 meters east and the total time is 15 seconds. Dividing 20 m by 15 s gives 1.33 m/s east. - 12
An object starts from rest and accelerates at 3 meters per second squared for 6 seconds. What is its final velocity, and what is the shape of its velocity-time graph during this interval?
The final velocity is 18 meters per second because the object starts at 0 m/s and gains velocity according to v = at, so 3 x 6 = 18 m/s. Its velocity-time graph is a straight line rising upward from the origin because constant acceleration produces a linear increase in velocity.