Displacement given time, initial velocity, and final velocity: delta s = 1/2 (v0 + vf) t. If v0 = 2 m/s, vf = 6 m/s, t = 4 s, what is delta s?

Displacement given time, initial velocity, and final velocity: delta s = 1/2 (v0 + vf) t. If v0 = 2 m/s, vf = 6 m/s, t = 4 s, what is delta s?

• A. 12 m
• B. 8 m
• C. 20 m
• D. 16 m

Answer: (D)

Displacement with constant acceleration equals the average velocity over the interval times the time taken. When acceleration is constant, the velocity changes linearly from v0 to vf, so the average velocity during the interval is (v0 + vf)/2. Compute the numbers: (v0 + vf) = 2 m/s + 6 m/s = 8 m/s, so the average velocity is 8/2 = 4 m/s. Then Δs = (4 m/s) × (4 s) = 16 m. So the displacement is 16 meters.

Displacement with constant acceleration equals the average velocity over the interval times the time taken. When acceleration is constant, the velocity changes linearly from v0 to vf, so the average velocity during the interval is (v0 + vf)/2.

Compute the numbers: (v0 + vf) = 2 m/s + 6 m/s = 8 m/s, so the average velocity is 8/2 = 4 m/s. Then Δs = (4 m/s) × (4 s) = 16 m.

So the displacement is 16 meters.