Question

A body of mass 3 kg travels according to the equation of displacement x=3t+4tsquare +5tcube find force acting on the body at t=2sec​

Answer 1

Given :-

Mass of Particle = m = 3 Kg

Position of particle = x = 5t³ + 4t² + 3t

Time = t = 2s

Here in this we will first differentiate w.r.t 't' in order to get Velocity and after getting Velocity we will again differentiate to get acceleration of the Particle at time, t = 2s.

v = dx/dt

v = d(5t³+4t²+3t)/dt

v = 15t² + 8t + 3

Again, Differentiating 'v' w.r.t 't' in order to get acceleration.

a = dv/dt

a = d(15t²+8t+3)/dt

a = 30t + 8

Putting, t = 2s.

a = 30(2) + 8

a = 68 ms-²

As we know that,

F = ma

F = 3(68)

F = 204 N.

Hence,

Force acting on the particle = F = 204 N.