Question

Is impulse change in momentum?

Answer 1

Step 1: Explanation:

If a force is applied to a body, the body accelerates in the direction of the applied force because of Newton's second law of motion.

Acceleration is defined as the rate of change in velocity, which may be expressed mathematically as:

$a=\frac{v-u}{t}$, Where, $a$= Acceleration, $v$= Final velocity, $u$= Initial velocity and $t$= Time

So,$F=ma$ can be written as follows:

$F=\frac{m\left(v-u\right)}{t}$, Where, $F$= Force

Since, $(mv–mu)$ denotes a change in momentum,

$F=\frac{mv-mu}{t}$…..(i)

If a force $F$ is applied to a body of mass m during a time interval$t$, and the change in velocity is$v$, then the impulse is given by,

$F=\frac{Changeofmomentum}{t}$….(ii)

Step 2: Solving from equation (i) and equation (ii),

Since,

$$\begin{gathered} Impulse=Fdt \\ I=m∆v \end{gathered}$$

Then,

$F=\frac{mv-mu}{t}$

Rearranging the equation, we get

$Ft=mv-mu$

The impulse refers to the quantity of ‘Force’ multiplied by ‘Time’.

Hence, the impulse is change a in momentum.