Speed, velocity and distance-time graphs
Grade 8 Science Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
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?
East is positive. Bo's ball rolls east at 3 m/s, hits a wall and rolls west at 3 m/s. The change takes 0.5 s. Acceleration is velocity change ÷ time. What is its size?
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?
A river flows east at 2 m/s. Luz paddles a canoe east at 3 m/s relative to the water. How fast does the canoe move relative to the bank, and which way?
- 1 m/s east: the speeds subtract, since the river works against the paddle
- 3 m/s east: the speed of the river does not change how the bank sees the canoe
- 1 m/s west: the river is stronger than the paddling and carries the canoe back
- 5 m/s east: the paddling and the current add together, since both point east
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 0 m/s; average velocity 0 m/s, since the object ends where it began
- 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
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?
- 3.5 m/s away from the start: 140 m of path covered in the full 40 s of the trip
- 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
- 1 m/s toward the start, the average of the velocities +3 m/s and −5 m/s on the graph
Pia graphs a walk with a rest in the middle. What is the average speed for the whole 40 s?
- 2 m/s: the average of the two moving speeds, 1 m/s and 3 m/s
- About 1.7 m/s: 50 m in the 30 s while the object was moving
- About 1.3 m/s: the average of the three speeds 1, 0 and 3 m/s
- 1.25 m/s: 50 m in 40 s, counting the rest as part of the trip
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 Ren claims that doubling the ramp height doubles the cart's average speed. Does the table support the claim?
- Yes: 20 cm is twice 10 cm, and 1.7 s is nearly twice as quick as 2.4 s
- No: ramp height has no effect on speed, since the cart finished the 1.2 m each time it rolled
- 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
Plan idea (example data)
car mass (g) wheels time for 2 m (s) X 100 plastic 2 Y 300 rubber 1.6 Tala wants to test whether a heavier car is faster. Which plan is fair and trustworthy?
- Use cars with the same wheels on one ramp, change only the mass, and time car Y three times and car X once
- Use cars of different masses on two different ramps, and time each car three times
- Use cars with different wheels on one ramp and the same mass, 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
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 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
- Both carts average 1.8 s, and the spread within each cart is as large as any gap
- 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