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 velocity (example data)

   time (s)	velocity (m/s)
   0	0
   1	1
   2	8
   3	27
   4	64

5. 4.

   Jun reads the velocity table. What are the average acceleration over 0 to 4 s and the acceleration at 2 s?

   • 16 m/s² on average; 7 m/s² at 2 s, from (8 − 1) ÷ 1
   • 16 m/s² on average and at 2 s, since a is steady
   • 16 m/s² on average; about 13 m/s² at 2 s
   • 13 m/s² on average; 16 m/s² at 2 s
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 area should use the start velocity: 2 × 4 = 8 m, not the final one
   • Nothing: the area under the line is 10 × 4
   • The time should be doubled, giving 80 m
   • The velocity was not 10 m/s all along; the area is 24 m
7. 6.

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

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

   Carts A and B start at the same spot at 0 s. Noah says they are side by side at 4 s, where the lines cross. Is that right?

   • No: A is ahead, since its line ends higher
   • No: they are not together, A has gone 16 m and B 8 m by then
   • No: equal velocity at 4 s, but B has gone 16 m and A only 8 m
   • Yes: the lines meet, so the carts are in the same place
9. 8.

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

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

10. A cart's position (example data)

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

11. 9.

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

    • Yes: the position changes just 1 m in the first second, so a is small
    • Yes: zero velocity at 0 s means zero acceleration at 0 s
    • No: the acceleration is 1 m/s², the position at 1 s
    • No: velocity rises 2 m/s each second from 0 s, so a = 2 m/s²
12. 10.

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

    • Yes: it moves backward, so its acceleration is negative, −1 m/s²
    • No: a = +3 m/s², the total rise in velocity over the 3 s
    • 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