Displacement and velocity, with a frame of reference

Answer Key - Grade 11 Science Worksheet

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

1. 1.

   East is positive. Ari's cart rolls 80 m east at 4 m/s, then 20 m west at 5 m/s. What is its average velocity for the whole trip?

   2.5 m/s
2. 2.

   East is positive. Esme's cart rolls 90 m east at 3 m/s, then 135 m west at 9 m/s. What is its average velocity for the whole trip?

   -1 m/s
3. 3.

   In the position-time graph, what is the cart's average velocity for the whole 12 s, Jun?

   • +2.25 m/s, the total distance ÷ time
   • −3 m/s, the slope of the last piece
   • −0.25 m/s, from a displacement of −3 m
   • 0 m/s, since the slopes +3, 0 and −3 average out
4. 4.

   Kira's boat heads straight across a 120 m wide river at 4.0 m/s relative to the water. The current is 3.0 m/s downstream. How long to cross, and how far downstream does it land?

   • 30 s, landing 90 m downstream
   • 24 s, landing 72 m downstream
   • 40 s, landing 120 m downstream
   • 30 s, landing 120 m downstream
5. 5.

   For the same boat, what are its speed relative to the bank and its direction measured from straight across, Luz?

   • 1.0 m/s, 37° downstream of straight across
   • 5.0 m/s, 53° downstream of straight across
   • 7.0 m/s, 37° downstream of straight across
   • 5.0 m/s, 37° downstream of straight across
6. 6.

   Milo hikes 6.0 km east in 2.0 h, then back 6.0 km west in 3.0 h. What are the average speed and average velocity?

   • Speed 2.4 km/h; velocity 0 km/h
   • Speed 2.4 km/h; velocity 2.4 km/h
   • Speed 2.5 km/h; velocity 0 km/h, from the mean of 3 and 2
   • Speed 0 km/h; velocity 0 km/h
7. 7.

   A drone flies 300 m east, then 400 m north, in 100 s. What are its displacement, average velocity and average speed, Noah?

   • 500 m at 53° north of east; velocity 5 m/s, speed 7 m/s
   • 100 m north of east; velocity 1 m/s, speed 7 m/s
   • 700 m north of east; velocity 7 m/s, speed 7 m/s
   • 500 m north of east; velocity 5 m/s, speed 5 m/s
8. 8.

   East is positive. Car A drives +25 m/s and truck B +18 m/s, with B 70 m ahead. How long until A reaches B, Ren?

   • 1.6 s: 70 ÷ (25 + 18)
   • 2.8 s: 70 ÷ 25, ignoring B
   • 10 s: A gains 7 m/s on B
   • 3.9 s: 70 ÷ 18, ignoring A
9. 9.

   The boat (4.0 m/s relative to the water) must land directly across a 120 m river with a 3.0 m/s current. How should Tala aim, and how long does it take?

   • Aim 49° upstream; about 45 s to cross
   • Aim straight across; 30 s, but it lands downstream
   • Aim 49° upstream; 30 s, using the full 4.0 m/s across
   • Aim 37° upstream; about 38 s to cross
10. 10.

    A plane heads north at 200 m/s in air. A wind blows east at 50 m/s. What is its ground speed, and how far east does it drift in 10 min, Zee?

    • 206 m/s; 30 km east
    • 250 m/s; 30 km east
    • 200 m/s; 30 km east
    • 206 m/s; 120 km east