Question

which is the correct formula for straight-line acceleration?
○ ( a = \frac{\triangle t}{\triangle vec{v}} )
○ ( a = \frac{v}{t} )
○ ( a = vec{v} \times t )
○ ( a = \frac{\triangle vec{v}}{\triangle t} )

Explanation:

To determine the correct formula for straight - line acceleration, we recall the definition of acceleration. Acceleration is defined as the rate of change of velocity with respect to time. The change in velocity is represented as $\Delta\vec{v}$ (where the vector symbol indicates that velocity is a vector quantity, and in straight - line motion, we can also think in terms of the change in speed in a direction) and the change in time is $\Delta t$.

• For the first option $a=\frac{\Delta t}{\Delta\vec{v}}$, this is the reciprocal of the correct relationship, so it is incorrect.
• The second option $a = \frac{v}{t}$ is incorrect because it does not account for the change in velocity. It would be the formula for a different quantity (if $v$ was initial velocity and $t$ was time, it would not represent acceleration correctly as acceleration is about the change in velocity).
• The third option $a=\vec{v}\times t$ is incorrect as multiplying velocity by time does not give acceleration.
• The fourth option $a=\frac{\Delta\vec{v}}{\Delta t}$ is correct because it represents the change in velocity ($\Delta\vec{v}$) divided by the change in time ($\Delta t$), which is the definition of acceleration.

Answer:

$a=\frac{\overrightarrow{\Delta v}}{\Delta t}$ (the fourth option)