A car starts from rest and accelerates at 4 m/s^2 for 6 s. What is its final velocity and the displacement during that interval?

A car starts from rest and accelerates at 4 m/s^2 for 6 s. What is its final velocity and the displacement during that interval?

• A. v = 24 m/s; displacement = 72 m
• B. v = 20 m/s; displacement = 60 m
• C. v = 28 m/s; displacement = 80 m
• D. v = 24 m/s; displacement = 120 m

Answer: (A)

Constant acceleration means velocity changes in a straight-line way over time. With v0 = 0, acceleration a = 4 m/s^2, and time t = 6 s, the final velocity is v = v0 + a t = 0 + 4 × 6 = 24 m/s. The displacement during this interval can be found from s = v0 t + (1/2) a t^2 = 0 + 0.5 × 4 × (6)^2 = 2 × 36 = 72 m. (An equivalent check uses the average velocity, v_avg = (v0 + v)/2 = 12 m/s, so s = v_avg × t = 12 × 6 = 72 m.)

Constant acceleration means velocity changes in a straight-line way over time. With v0 = 0, acceleration a = 4 m/s^2, and time t = 6 s, the final velocity is v = v0 + a t = 0 + 4 × 6 = 24 m/s. The displacement during this interval can be found from s = v0 t + (1/2) a t^2 = 0 + 0.5 × 4 × (6)^2 = 2 × 36 = 72 m. (An equivalent check uses the average velocity, v_avg = (v0 + v)/2 = 12 m/s, so s = v_avg × t = 12 × 6 = 72 m.)