Exercises: Average Speed, Velocity, and Distance-Time Graphs

Emma rides her bike along a straight path in a park. She travels 1,200 meters in 300 seconds. Write the formula for average speed and calculate Emma's average speed in meters per second (m/s).

Mateo says, "Speed and velocity are exactly the same thing." Explain in your own words the difference between speed and velocity. Then classify each of the following as speed or velocity: (a) 15 m/s, (b) 15 m/s north.

A distance-time graph shows a straight horizontal line (flat) for a stretch of time. What does a horizontal line on a distance-time graph tell you about the motion of the object during that time? Explain how you know.

During a track meet, Aaliyah runs 4 laps around a circular track. Each lap is 400 meters, and her total time is 6 minutes 40 seconds.

(a) Convert her time to seconds.

(b) Calculate her average speed in m/s.

(c) She ends at the same spot where she started. What is her displacement, and what does this say about her average velocity for the whole run?

The table shows the position of a toy car moving along a straight line, measured from a starting mark.

(a) Calculate the average speed between 0 s and 8 s.

(b) Describe what a distance-time graph of this data would look like.

(c) Is the car's speed constant? Justify your answer using the table.

Jayden walks 300 meters east from his house to a store in 200 seconds. Then he walks 100 meters west toward a friend's house in 100 seconds.

(a) What total distance did he travel?

(b) What is his displacement from his house at the end?

(c) Calculate his average speed for the whole trip.

(d) Calculate the magnitude of his average velocity and give its direction.

A distance-time graph for Sofia's bus ride has three segments:

• Segment A: from 0 s to 60 s, the distance increases from 0 m to 600 m in a straight line.

• Segment B: from 60 s to 90 s, the distance stays at 600 m.

• Segment C: from 90 s to 150 s, the distance increases from 600 m to 1,200 m in a straight line.

(a) Calculate the speed in each segment.

(b) Describe what the bus is doing in each segment and compare the slopes of A and C.

(c) Calculate the average speed for the whole 150 s.

(d) Explain why the average speed for the whole trip is not the average of the speeds in segments A and C.

Marcus and Priya start from the same point and move in a straight line. Marcus's graph is a straight line from (0 s, 0 m) to (20 s, 100 m). Priya's graph is a straight line from (0 s, 0 m) to (10 s, 20 m), then a steeper straight line from (10 s, 20 m) to (20 s, 120 m).

(a) Find Marcus's speed.

(b) Find Priya's speed in each part of her trip.

(c) Who is ahead at 10 s? Who is ahead at 20 s?

(d) At what time, if any, did Priya catch up with Marcus? Support your answer with calculations or the graphs.