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:

1. "displacement = final displacement - initial displacement" is incorrect as it's a trivial definition, not a useful kinematic equation.
2. "velocity = displacement/time" is the formula for average velocity (when velocity is constant), but in kinematics with acceleration, the standard equations are different. However, if we consider uniform motion (constant velocity), this is correct, but usually, the kinematic equations for motion with constant acceleration are more common. Wait, no—actually, the key here is to recall the basic kinematic equations. Wait, the third option: "acceleration = (final velocity - initial velocity)/time" is the definition of average acceleration (for constant acceleration, it's the same as instantaneous acceleration). But the fourth option: "displacement = (initial velocity × time) + (1/2)(acceleration)(time²)" is one of the fundamental kinematic equations for motion with constant acceleration (the second equation of motion, \( s = ut + \frac{1}{2}at^2 \), where \( s \) is displacement, \( u \) is initial velocity, \( a \) is acceleration, \( t \) is time). The fifth option: "acceleration = ((final velocity)² - (initial velocity)²)/(2 × displacement)" is also a kinematic equation (\( v^2 = u^2 + 2as \) rearranged), but the fourth option is the second equation of motion, which is a basic one used when we know initial velocity, time, and acceleration to find displacement. Wait, but the question is "Which Equation should you use?"—probably referring to the kinematic equations for motion with constant acceleration. Let's check each:

• First option: Trivial, not a useful equation for calculation.
• Second option: Average velocity (constant velocity), not for accelerated motion.
• Third option: Definition of average acceleration (correct for constant acceleration, \( a = \frac{v - u}{t} \)).
• Fourth option: \( s = ut + \frac{1}{2}at^2 \) (correct kinematic equation for displacement with constant acceleration).
• Fifth option: \( a = \frac{v^2 - u^2}{2s} \) (also correct, but used when displacement and velocities are known).

But the fourth option is the standard second equation of motion, which is widely used. Wait, but maybe the question is about the correct kinematic equation. Let's re-express:

The fourth option: displacement = (initial velocity × time) + (1/2)(acceleration)(time²) is the correct kinematic equation for motion with constant acceleration (the second equation, \( s = ut + \frac{1}{2}at^2 \)).

Wait, but let's check the third option: acceleration = (final velocity - initial velocity)/time is \( a = \frac{v - u}{t} \), which is the definition of average acceleration (correct for constant acceleration). But the fourth option is a displacement equation. Depending on the context, but in typical kinematics problems, the displacement equation \( s = ut + \frac{1}{2}at^2 \) is a key equation. However, maybe the question is about the correct formula. Let's see the options again:

1. displacement = final - initial: trivial, not a formula for calculation.
2. velocity = displacement/time: average velocity (constant velocity).
3. acceleration = (v - u)/t: correct for average acceleration (constant a).
4. displacement = ut + 0.5at²: correct kinematic equation.
5. acceleration = (v² - u²)/(2s): correct kinematic equation.

But the fourth option is the second equation of motion, which is a fundamental one. So the correct answer is the fourth option: displacement = (initial velocity × time) + (1/2)(acceleration)(time²)

Answer:

The correct option is the one with "displacement = (initial velocity x time) + (1/2)(acceleration)(time^2)" (the fourth option in the list, considering the order: first option is displacement = final - initial, second is velocity = displacement/time, third is acceleration = (v - u)/time, fourth is displacement = ut + 0.5at², fifth is a = (v² - u²)/(2s)). So the answer is the option: displacement = (initial velocity x time) + (1/2)(acceleration)(time^2)