Question

which equation should you use? *
displacement = final displacement - initial displacement
velocity = displacement/time
acceleration = (final velocity - initial velocity)/time
displacement = (initial velocity x time) + (1/2)(acceleration)(time^2)
acceleration = ((final velocity)^2 - initial velocity)^2)/(2 x displacement)

Explanation:

To determine the correct equation, we analyze each option based on kinematic equations (for motion with constant acceleration):

1. "displacement = final displacement - initial displacement": This is a trivial definition (displacement is the change in position), not a useful kinematic equation for motion analysis. Eliminate.
2. "velocity = displacement/time": This is the formula for average speed/velocity (for constant velocity), not a kinematic equation for accelerated motion. Eliminate.
3. "acceleration = (final velocity - initial velocity)/time": This is the definition of average acceleration (\( a = \frac{v_f - v_i}{t} \)) for motion with constant acceleration. This is a fundamental kinematic equation.
4. "displacement = (initial velocity × time) + (1/2)(acceleration)(time²)": This is the kinematic equation for displacement (\( s = v_i t + \frac{1}{2} a t^2 \)), but it applies to constant acceleration (e.g., free fall). However, the question asks which equation to use, and the third option (acceleration formula) is a more basic definition.
5. "acceleration = ((final velocity)² - (initial velocity)²)/(2 × displacement)": This is another kinematic equation (\( a = \frac{v_f^2 - v_i^2}{2s} \)), but it is derived from the others and less fundamental than the acceleration definition.

The third option ("acceleration = (final velocity - initial velocity)/time") is the definition of acceleration (change in velocity over time) and is the most fundamental equation here.

Answer:

The correct option is the one with: acceleration = (final velocity - initial velocity)/time (the third option in the list).