# Worksheet: Velocity–Time Graphs

In this worksheet, we will practice calculating the displacement or acceleration of a particle moving in a straight line from its velocity–time graph.

Q1:

The given velocity-time graph represents a particle moving in a straight line. Determine its displacement at . Q2:

Given the velocity-time graph for a particle that moved in a straight line, determine its acceleration at . Q3:

Given the velocity-time graph of a particle moving in a straight line, determine the displacement of the particle within the time interval . Q4:

Given the velocity-time graph of a particle moving in a straight line, determine the distance covered by the particle within the time interval . Q5:

The given velocity-time graph represents a particle moving in a straight line. Determine its displacement at . Q6:

Given the velocity-time graph of a particle moving in a straight line, determine the distance covered by the particle within the time interval . Q7:

Given the velocity-time graph of a particle moving in a straight line, determine the distance covered by the particle within the time interval . Q8:

Given the velocity-time graph of a particle moving in a straight line, determine the displacement of the particle within the time interval . Q9:

Given the velocity-time graph of a particle moving in a straight line, determine the displacement of the particle within the time interval . Q10:

Given the velocity-time graph of a particle moving in a straight line, determine the displacement of the particle within the time interval . Q11:

The figure shown is a velocity-time graph for two cars moving in a straight line. The movement of car is represented by the green line, and the movement of car by the blue line. Determine how long it took for the two cars to meet again, given that they started from the same point. Q12:

The figure shown is a speed-time graph for a body moving in a straight line. Given that its initial speed was 5 m/s, determine the body’s acceleration during the part of the journey where the body was accelerating. Q13:

The figure shown is a velocity-time graph for a body moving in a straight line with an initial velocity of 10 m/s. Determine the total distance covered by the body, given that it came to rest 100 seconds after it started moving. Q14:

The figure shown is a velocity-time graph for a body moving in a straight line. Determine the deceleration of the body during the final section of its movement, given that it came to rest 100 seconds after it started moving. Q15:

Three cars, A, B, and C, are being driven along a straight road. The following graphs show how the velocity of each car changes once the driver sees that the traffic lights are red. Which car stops in the shortest distance?

• ACar B
• BCar C
• CCar A

Q16:

Below is a velocity–time graph of a marathon runner running down a racetrack over a period of 8 seconds. Find the acceleration of the runner during the first 2 seconds.

Find the distance covered by the runner over the 8-second period.

Q17:

The acceleration of a moving body can be calculated graphically by .

• Athe area under the displacement–time curve
• Bthe area under the velocity–time curve
• Cthe slope of the velocity–time curve
• Dthe slope of the displacement–time curve

Q18:

The figure shows a velocity time graph of a particle moving in a straight line. When is the particle’s acceleration zero? • Afrom to and from to
• Bfrom to
• Cfrom to
• Dfrom to

Q19:

Michael made a 60-minute trip to town. The given graph shows the distance he was from his house throughout his trip. He stopped at two shops. At what times was that?

• A and
• B and
• C and
• D and
• E and

At some point, he changed direction without stopping first. When was that?

• A
• B
• C
• D
• E

At what times was he moving toward his house?

• A and
• B and
• C and
• D and
• E and

At which minute was he moving fastest?

• A
• B
• C
• D
• E

Q20:

The figure shows a velocity-time graph for a car moving in a straight line. Given that is measured in metres per second and in seconds, determine when the car is moving forward. • Afrom to and from to
• Bfrom to
• Cfrom to and from to
• Dfrom to

Q21:

The three graphs in the figure show the position of a particle, its velocity, and its acceleration against time, respectively. Identify each graph. • ADisplacement–time graph: red, velocity–time graph: blue, acceleration–time graph: green
• BDisplacement–time graph: blue, velocity–time graph: red, acceleration–time graph: green
• CDisplacement–time graph: red, velocity–time graph: green, acceleration–time graph: blue
• DDisplacement–time graph: green, velocity–time graph: blue, acceleration–time graph: red
• EDisplacement–time graph: green, velocity–time graph: red, acceleration–time graph: blue

Q22:

The figure shows a velocity-time graph for a particle moving in a straight line. When is the acceleration of the particle negative? • Afrom to
• Bfrom to and from to
• Cfrom to , from to , and from to
• Dfrom to and from to

Q23:

Which color graph represents the path of a particle whose velocity is increasing? • AGreen
• BBlue
• CRed
• DYellow

Q24:

Which colour graph represents the path of a particle with uniform acceleration? • Ayellow
• Bred
• Cgreen
• Dblue