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 solve this, we analyze each option based on kinematic equations (for constant acceleration motion):

1. Option 1: displacement = final displacement - initial displacement

This is trivial (displacement is defined as the change in position, so \( \Delta x = x_f - x_i \)), but it is not a kinematic equation for motion with acceleration. It is just a definition.

1. Option 2: velocity = displacement/time

This is the formula for average speed/velocity (when velocity is constant). For motion with acceleration, this is only valid for average velocity (\( v_{\text{avg}} = \frac{\Delta x}{t} \)), but it is not a standard kinematic equation for accelerated motion.

1. Option 3: acceleration = (final velocity - initial velocity)/time

This is the definition of average acceleration: \( a = \frac{v_f - v_i}{t} \) (valid for constant acceleration, as it becomes instantaneous acceleration in the limit). This is a fundamental kinematic equation.

1. Option 4: displacement = (initial velocity × time) + (1/2)(acceleration)(time²)

This is the kinematic equation for displacement in uniformly accelerated motion: \( \Delta x = v_i t + \frac{1}{2} a t^2 \). It is valid for constant acceleration.

1. Option 5: acceleration = ((final velocity)² - (initial velocity)²)/(2 × displacement)

This is the kinematic equation \( v_f^2 = v_i^2 + 2 a \Delta x \), rearranged to \( a = \frac{v_f^2 - v_i^2}{2 \Delta x} \). It is valid for constant acceleration.

Choosing the Correct Equation

The question asks “Which Equation should you use?” — but without context (e.g., what quantity you need to find, or known variables), we assume the most fundamental or commonly tested kinematic equation.

• The definition of acceleration (Option 3: \( a = \frac{v_f - v_i}{t} \)) is a core kinematic relation.
• The displacement equation (Option 4: \( \Delta x = v_i t + \frac{1}{2} a t^2 \)) is also fundamental.
• The velocity-displacement equation (Option 5) is derived from the others.

If we assume the question is about the definition of acceleration (a basic kinematic relation), the correct option is:

The equation \( \text{acceleration} = \frac{\text{final velocity} - \text{initial velocity}}{\text{time}} \) (Option 3) is the definition of average acceleration (valid for constant acceleration) and is a fundamental kinematic equation.

Answer:

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