Speed, velocity and distance-time graphs

Answer Key - Grade 8 Science Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   East is positive. Ari's cart rolls east at 6 m/s, hits a bumper and rolls west at 4 m/s. The change takes 2 s. Acceleration is velocity change ÷ time. What is its size?

   5 m/s²
2. 2.

   East is positive. Esme's wagon rolls east at 8 m/s, nudges a post and rolls west at 2 m/s. The change takes 4 s. Acceleration is velocity change ÷ time. What is its size?

   2.5 m/s²
3. 3.

   Train A moves east at 25 m/s and train B moves east at 20 m/s on parallel tracks. How does train A move as seen from train B, Jun?

   • 25 m/s east: the motion of train B does not change how train A looks
   • 5 m/s west: train A seems to slide backward past the windows of train B
   • 45 m/s east: the two speeds add, since both trains move toward the east
   • 5 m/s east: train A pulls ahead of train B by 5 m each second, since the speeds subtract
4. 4.

   Kira rides a train going north at 30 m/s. Another train passes on a parallel track going south at 20 m/s. How does the other train seem to move?

   • 50 m/s south: the speeds of the two trains add, since they move in opposite directions
   • 50 m/s north: the other train seems to move the same way as the rider's train
   • 20 m/s south: the rider's own motion does not change how the other train looks
   • 10 m/s south: the speeds are subtracted, since the trains are on parallel tracks
5. 5.

   East is positive. Milo walks out, rests, and walks back. What are the average speed and average velocity for the whole 60 s?

   • Average speed 3 m/s; average velocity 0 m/s, using the 40 s the object was moving
   • Average speed 2 m/s; average velocity 2 m/s, since the object moved a total of 120 m in 60 s
   • Average speed 2 m/s; average velocity 0 m/s, since the net change in position is 0 m
   • Average speed 0 m/s; average velocity 0 m/s, since the object ends where it began
6. 6.

   Away from the start is positive. Noah graphs a trip out and part way back. What is the average velocity for the whole 40 s?

   • 1 m/s toward the start, the average of the velocities +3 m/s and −5 m/s on the graph
   • 1 m/s away from the start: 40 m of net movement in 40 s, not the 140 m of path
   • 4 m/s away from the start, the average of the speeds 3 m/s and 5 m/s
   • 3.5 m/s away from the start: 140 m of path covered in the full 40 s of the trip
7. 7.

   Pia graphs a walk with a rest in the middle. What is the average speed for the whole 40 s?

   • 1.25 m/s: 50 m in 40 s, counting the rest as part of the trip
   • About 1.7 m/s: 50 m in the 30 s while the object was moving
   • 2 m/s: the average of the two moving speeds, 1 m/s and 3 m/s
   • About 1.3 m/s: the average of the three speeds 1, 0 and 3 m/s

8. Read this first

   Cart down a ramp (example data)

   ramp height (cm)	time for 1.2 m (s)
   10	2.4
   20	1.7
   30	1.4

9. 8.

   Ren claims that doubling the ramp height doubles the cart's average speed. Does the table support the claim?

   • No: from 10 cm to 20 cm the speed rises from 0.50 to about 0.71 m/s, short of double
   • Yes: the time falls each time the height rises, so the speed doubles each time
   • No: ramp height has no effect on speed, since the cart finished the 1.2 m each time it rolled
   • Yes: 20 cm is twice 10 cm, and 1.7 s is nearly twice as quick as 2.4 s

10. Plan idea (example data)

    car	mass (g)	wheels	time for 2 m (s)
    X	100	plastic	2
    Y	300	rubber	1.6

11. 9.

    Tala wants to test whether a heavier car is faster. Which plan is fair and trustworthy?

    • Use cars with different wheels on one ramp and the same mass, and time each car three times
    • Use cars of different masses on two different ramps, and time each car three times
    • Use cars with the same wheels on one ramp, change only the mass, and time each car three times
    • Use cars with the same wheels on one ramp, change only the mass, and time car Y three times and car X once

12. Light and heavy carts, three trials each (example data)

    trial	light cart (s)	heavy cart (s)
    1	1.8	1.9
    2	1.7	1.8
    3	1.9	1.7

13. 10.

    Zee claims heavy carts roll faster. Which statement do three trials of each cart support?

    • The data are useless, because no two trials gave exactly the same time as each other
    • The light cart is faster, because it was ahead in two of the three trials, 1.8 s and 1.7 s
    • The heavy cart is faster, because it had the quickest single trial, 1.7 s, of the six trials
    • Both carts average 1.8 s, and the spread within each cart is as large as any gap