Position-time and velocity-time graphs

Answer Key - Grade 11 Science Worksheet - Challenge Me

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

1. 1.

   Ari's cart A starts 24 m behind cart B. A rolls at 7 m/s and B at 5 m/s, both the same way. After how many seconds does A catch B?

   12 s
2. 2.

   Bo's cart A starts 30 m behind cart B. A rolls at 8 m/s and B at 2 m/s, both the same way. After how many seconds does A catch B?

   5 s
3. 3.

   Esme's cart A starts 20 m behind cart B. A rolls at 6 m/s and B at 4 m/s, both the same way. After how many seconds does A catch B?

   10 s

4. Read this first

   A cart's position (example data)

   time (s)	position (m)
   0	0
   1	3
   2	4
   3	3
   4	0
   5	−5

5. 4.

   Kira reads the cart's position table. When does the cart turn around, and what are the displacement and distance from 0 s to 5 s?

   • At 4 s, where it is back at 0 m; displacement −5 m, distance 13 m
   • At 2 s; displacement −5 m, distance 13 m
   • At 2 s; displacement −5 m, distance 5 m
   • At 2 s; displacement 4 m, distance 4 m, from the peak
6. 5.

   Luz says the cart went 10 × 4 = 40 m, using the final velocity and the time. What is wrong with the claim?

   • The velocity was not 10 m/s all along; the area is 24 m
   • The time should be doubled, giving 80 m
   • Nothing: the area under the line is 10 × 4
   • The area should use the start velocity: 2 × 4 = 8 m, not the final one
7. 6.

   Milo says a cart rolled over a hill, since its position-time graph is hill-shaped. Which reply fits the graph?

   • Yes: the cart slows at the top, where the line peaks
   • No: it rolled out, then stopped for 3 s
   • No: it rolled out at 2 m/s, then back at 2 m/s; the graph is not a path
   • Yes: the graph rises and falls, so the track itself must rise and then fall
8. 7.

   Pia says the cart is slowing down because its velocity is negative. Which reply fits the graph?

   • No: it speeds up, and its acceleration is +1 m/s²
   • Yes: the line slopes down, and down means slowing
   • Yes: a negative velocity means the cart must be slowing down
   • No: its speed grows from 2 to 6 m/s while moving backward

9. A cart's position (example data)

   time (s)	position (m)
   0	0
   1	1
   2	4
   3	9
   4	16

10. 8.

    Ren says the cart's acceleration at 0 s is zero, since its velocity is zero then. Which reply fits the position table?

    • No: velocity rises 2 m/s each second from 0 s, so a = 2 m/s²
    • No: the acceleration is 1 m/s², the position at 1 s
    • Yes: zero velocity at 0 s means zero acceleration at 0 s
    • Yes: the position changes just 1 m in the first second, so a is small
11. 9.

    Tala says the cart's acceleration is negative because it moves backward. Which reply fits the velocity-time graph?

    • No: velocity rises −5 to −2 m/s, so a = +1 m/s² and it slows
    • Yes: a = (−5 − (−2)) ÷ 3 = −1 m/s², last minus first
    • No: a = +3 m/s², the total rise in velocity over the 3 s
    • Yes: it moves backward, so its acceleration is negative, −1 m/s²
12. 10.

    A cart speeds up from rest at 2 m/s² for 4 s, then coasts at constant velocity for 6 s. What are its displacement and average velocity over the 10 s, Zee?

    • 64 m, an average velocity of 6.4 m/s
    • 40 m, an average velocity of 4 m/s
    • 48 m, an average velocity of 4.8 m/s
    • 80 m, an average velocity of 8 m/s