Question

A body is accelerated by applying a force of $30$N. The change in the momentum of the body after $2$ sec is?

• A. $7.5$ kg-m/s
• B. $30$ kg-m/s
• C. $120$ kg-m/s
• D. $60$ kg-m/s

Answer 1

Answer: (D)

$60$ kg-m/s

We know force $F=mass\times acceleration$-------(1)

Given time = $2$ seconds

We can rewrite the equation (1) as

$Force=mass\times \frac{\text{Final(v)-Initial velocity(u)}}{\text{Time(t)}}$--------(2)

Also change in momentum $dp=p_{final}-p_{initial}$= $mass\times changeinvelocity$

Equation (2) becomes $F=\frac{dp}{dt}$

$Fdt=dp$

Integrating the above equation we get:

$F{\int }_0^{2}dt={\int }_{p_i}^{p_f}dp$

$30\times 2$ = $P_f-P_i$

Therefore change in momentum = $60$ kg m/s