Speed Time Graphs

Practice Questions:

1. What’s the initial speed of the car?
2. During which time interval is the car moving at constant speed?
3. Calculate the acceleration during the first 20 seconds
4. Calculate the total distance traveled
5. What’s happening to the car’s motion in the last 20 seconds?
6. What’s the car’s maximum speed?
7. Calculate the average speed for the entire journey

Answers

(1) Initial speed = 10 m/s (we read this from vertical axis at time = 0 seconds)

(2) Constant speed period is between 20-40 seconds and 30 m/s (the flat horizontal line)

(3) Acceleration between 0 and 20 seconds is:

• Acceleration = Change In Speed
• Change in speed = Final Speed – Starting Speed = 30m/s – 10m/s = 20 m/s
• Time taken = 20s
• Acceleration = Change in speed ÷ Time taken = 20 ÷ 20 = 1 m/s²

(4) Total distance = The full area under graph

• First section (triangle) = ½ Base x Height = ½ × 20 × 20 = 200m
• Middle section (rectangle): 20 × 30 = 600m
• Last section (triangle) = ½ Base x Height = ½ × 20 × 20 = 200m
• Total = 200 + 600 + 200 = 1000 meters

(5) The car is decelerating from 30 m/s to 10 m/s (the last downward slope)

(6) Maximum speed = 30 m/s (highest point on graph)

(7) Average speed = Total distance ÷ Total time

• = 1000 ÷ 60
• = 5.27 m/s