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Grade 8 · lesson 3 of 4

Track Velocity through Slowing and Reversal

Use v = v0 + at when acceleration is constant.

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Supplied materials

  • Use the supplied fictional observations or model. Paper and pencil are optional; spoken answers are welcome. No equipment or real experiment is needed.

Learn the idea

Velocity includes direction; speed is its magnitude. Choose right positive and use v = v0 + at for constant acceleration. A right-moving cart with leftward acceleration initially slows. If that acceleration continues long enough, its velocity can reach zero and then become leftward. It does not automatically reverse as soon as the force points left.

A fictional cart starts at +6 m/s and has constant a = −2 m/s². There are no unlisted horizontal effects, and the mass and net force stay constant over the stated interval. At 1, 2, 3, and 4 seconds, velocities are +4, +2, 0, and −2 m/s. Speeds are 4, 2, 0, and 2 m/s: after stopping at 3 seconds, it gains speed leftward.

  1. Write v0 = +6 m/s and a = −2 m/s².
  2. Calculate v at 1, 2, 3, and 4 seconds.
  3. Label positive, zero, and negative velocities with directions.
  4. Describe the separate periods before and after the zero-velocity instant.
Worked example

See the method in action

At 4 s, v = 6 + (−2)(4) = −2 m/s, left. The cart slows for its first 3 seconds, momentarily stops, then moves left if the acceleration continues.

Your turn

Check your reasoning

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What is the cart’s velocity after 2 seconds in the supplied model?

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See the answer and explanation

2 m/s right

6 + (−2)(2) = +2 m/s. It is still moving right, but slower than initially.

Take it further

Change starting velocity to +10 m/s with the same −2 m/s² acceleration. It reaches zero after 5 s; at 4 s it still moves right at +2 m/s.

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