A particle of mass 2 kg is at rest initially A force of magnitude F is applied on the - Physics - Basic Mathematics(Pre-requisite)

Question

A particle of mass 2 kg is at rest initially A force of magnitude F
is applied on the particle such that the particle starts moving
along the X - axis and its displacement is given by x = 2 + 3t +
4t?

calculate the magnitude of
i) the velocity of the particle at t = 3s
ii) acceleration of the particle at t = 3s
iii)force(F) applied on the particle

Sanat K Mukherjee · Accepted Answer

Given,
Mass of the particle, m = 2 kg
displacement pf the particle provided in the question is x = 2 + 3t + 4tIt must bex = 2 + 3t + 4t2 or x = 2 + 3t2 + 4t (otherwise the displaement must have been stated x=2+7t)Assuming x = 2 + 3t + 4t2, the question is soled as follows:
i) velocity, v=dxdt=3+8tAt, t=3s, v=3+24=27m/sii) Acceleration, a=dvdt=8acceleration remains constant and its value at all times including t=3s is 8m/s2iii) Force applied on the particle, F=ma=2×8=16N

Regards