A car accelerates uniformly from rest to 20 m/s in 5 s. What is the average acceleration, and what distance is traveled during this time (initial speed is 0)?

• A. a = 4 m/s^2; s = 50 m
• B. a = 2 m/s^2; s = 25 m
• C. a = 6 m/s^2; s = 100 m
• D. a = 4 m/s^2; s = 25 m

Answer: (A)

Uniform acceleration means the velocity changes at a constant rate, so the acceleration is the change in velocity divided by the time taken. From rest to 20 m/s in 5 seconds, the average acceleration is 20 / 5 = 4 m/s^2.

To find distance with constant acceleration from rest, use s = ut + (1/2) a t^2. With initial speed u = 0 and a = 4, this gives s = 0 + (1/2) × 4 × (5)^2 = 2 × 25 = 50 m.

So the car accelerates at 4 m/s^2 and travels 50 m in that 5-second interval. The other possibilities would imply a different final speed after 5 seconds or a different distance under the same conditions, so they don’t match the given information.