The displacement of a particle along a straight time at line t is given by ,x=4+2t`+3t^2+4t^3`.Find acceleration fo the particle at t=2 second.

A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion :- y=a sin 2pi t//T (a = maximum displacement of the particle, v = speed of the particle. T= time-period of motion). Rule out the wrong formulas on dimensional grounds.

A particle is moving in a straight line such that its displacement s at an instant of time t is given by the relation s = 3t^2 + 4 t + 5 Find the initial velocity of the particle.

Displacement s of a particle at time t is expressed as s=1/2t^3-6t . Find the acceleration at the time when the velocity vanishes (i.e., velocity tends to zero).

If the displacement of a particle is givne by s=((1)/(2)t^(2)+4sqrtt)m . Find the velocity and acceleration at t = 4 seconds.

The displacement of a particle is given by x = (t-2)^2 where x is in metres and t in seconds. The distance covered by the particle in first 4 seconds is

The velocity of a body of mass 2 kg as a function of t is given by vec v (t) = 2t hat i + t^2 hatj . Find the momentum and the force acting on it, at time t = 2s.