Question

A variable force (24t2 – 8t) Newton is acting
on a particle. The impulse imparted to it in
first two seconds will be:​

Answer 1

Answer:

Integration should be used here to get the answer as force is variable.

Answer 2

Answer :

A variable force acting on a particle is given by

• F = 24t² - 8t

We have to find impulse imparted to it in first two seconds$.$

★ Impulse is measured as the product of applied force and time.

Mathematically, J = F t

SI unit : kg m/s or N s

$:\implies\tt\:dJ=F\:dt$

$:\implies\tt\:dJ=(24t^2-8t)\:dt$

By integrating both sides, we get

$\displaystyle{:\implies\tt\:\int\limits_{0}^{J}\:dJ=\int\limits_{0}^{2}(24t^2-8t)\:dt}$

$:\implies\tt\:J=\bigg[\dfrac{24t^3}{3}-\dfrac{8t^2}{2}\bigg]_{0}^{2}$

$:\implies\tt\:J=\big[8t^3-4t^2\big]_0^2$

$:\implies\tt\:J=8(2^3-0^3)-4(2^2-0^2)$

$:\implies\tt\:J=8(8)-4(4)$

$:\implies\tt\:J=64-16$

$:\implies\:\boxed{\gray{\bf{J=48\:kg-ms^{-1}}}}$