Question

1. which of the following equations accurately defines acceleration?

$overrightarrow { a } =\frac { overrightarrow { s } }{ d }$
$overrightarrow { a } =\frac { \delta \overrightarrow { v } }{ \delta t }$
$overrightarrow { a } =\frac { \overrightarrow { d } }{ \delta t }$
$overrightarrow { a } =\frac { \overrightarrow { d } }{ v }$

Explanation:

Step1: Recall the definition of acceleration

Acceleration is the rate of change of velocity.

Step2: Analyze each option

• Option 1: $\vec{a}=\frac{\vec{v}}{d}$ is not the correct formula for acceleration. Velocity divided by distance has no physical meaning as acceleration.
• Option 2: $\vec{a}=\frac{\Delta\vec{v}}{\Delta t}$ is correct. Here, $\Delta\vec{v}$ is the change in velocity and $\Delta t$ is the change in time. Acceleration is defined as the change in velocity per unit time.
• Option 3: $\vec{a}=\frac{\vec{d}}{\Delta t}$ gives velocity (if $\vec{d}$ is displacement), not acceleration.
• Option 4: $\vec{a}=\frac{\vec{d}}{v}$ has no physical significance as an acceleration formula.

Answer:

$\vec{a}=\frac{\Delta\vec{v}}{\Delta t}$ (the second option)