Which expression gives displacement when final velocity, acceleration, and time are known?

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Multiple Choice

Which expression gives displacement when final velocity, acceleration, and time are known?

Explanation:
When acceleration is constant, displacement over a time interval can be expressed using the final velocity, acceleration, and time. Use the relation v_f = v0 + a t to solve for the initial velocity: v0 = v_f − a t. Plugging into s = v0 t + (1/2) a t^2 gives s = (v_f − a t) t + (1/2) a t^2 = v_f t − (1/2) a t^2. This form uses only the given quantities v_f, a, and t, so it directly provides the displacement. The other forms require knowledge of the initial velocity v0, or are not specific enough to yield displacement with only v_f, a, and t.

When acceleration is constant, displacement over a time interval can be expressed using the final velocity, acceleration, and time. Use the relation v_f = v0 + a t to solve for the initial velocity: v0 = v_f − a t. Plugging into s = v0 t + (1/2) a t^2 gives s = (v_f − a t) t + (1/2) a t^2 = v_f t − (1/2) a t^2. This form uses only the given quantities v_f, a, and t, so it directly provides the displacement.

The other forms require knowledge of the initial velocity v0, or are not specific enough to yield displacement with only v_f, a, and t.

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