An object starts from rest and moves with constant acceleration a. After time t, its displacement s is given by which expression?

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Multiple Choice

An object starts from rest and moves with constant acceleration a. After time t, its displacement s is given by which expression?

Explanation:
Starting from rest with constant acceleration, velocity increases linearly with time: v = a t. The displacement is the area under the velocity–time graph from 0 to t, which is a triangle with base t and height a t. Its area is (1/2) × base × height = (1/2) a t^2. Equivalently, using s = ut + (1/2) a t^2 with u = 0 gives s = (1/2) a t^2. The other forms don’t directly give distance here: s = a t would have the wrong units (velocity), and s = v t assumes constant velocity. So the correct expression is s = (1/2) a t^2.

Starting from rest with constant acceleration, velocity increases linearly with time: v = a t. The displacement is the area under the velocity–time graph from 0 to t, which is a triangle with base t and height a t. Its area is (1/2) × base × height = (1/2) a t^2. Equivalently, using s = ut + (1/2) a t^2 with u = 0 gives s = (1/2) a t^2. The other forms don’t directly give distance here: s = a t would have the wrong units (velocity), and s = v t assumes constant velocity. So the correct expression is s = (1/2) a t^2.

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