Chapter 3, Problem 53A

To determine

To explain: The relationship between acceleration and velocity.

Explanation of Solution

Introduction:

Acceleration:

It is the change in velocity with respect to time. It is a vector quantity. It can be positive, negative or even zero.

When, velocity of the object increases in any interval of time then acceleration will be positive.

If velocity is decreases in any interval, then acceleration will be negative and if velocity is constant it will be zero.

Velocity:

It is the change in distance with respect to time. It is also a vector quantity.

Mathematically, the rate at which velocity change with time is acceleration.

  $a=\frac{d}{dt}\left(v\right)$

Here, $a$ is acceleration and $\frac{d}{dt}\left(v\right)$ is the rate of change of velocity.

From classical physics,

According to first equation of motion, the acceleration and velocity is related as

  $\begin{array}{l}v=u+at\\ \Rightarrow a=\frac{v-u}{t}\end{array}$

Here, u is the initial velocity of object, v is the final velocity and t is time interval.

So, acceleration = Change in velocity / Change in time