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

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

• A. Delta s = vf t - (1/2) a t^2
• B. Delta s = v0 t + (1/2) a t^2
• C. Delta s = (1/2) (vf + v0) t
• D. Delta s = distance traveled

Answer: (A)

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.