Question

5) the acceleration of the particle at time t is given by a = [18cos 3t, -8sin2t, 6t]. If the velocity v and displacement r be zero at t=0. Evaluate v and r at any time t.

Answer 1

a=dv/dt and v=dr/dt here a is acceleration and v is velocity and r is displacement

then dv= adt for finding a integrate w.r.t. time and we get

v=6sin3t i+4cos2t j + 3t^2+c

and then at t=0 v=0then find the value of c .u get c=-4 put it the above equation u ger the required velocity.

v=6sin3t i+ 4cos2t j + 3t^2-4

dr= vdt

r=-2cos3t i +2sin2t j+t^3+c

at t=0 r=0 we get c=2 putting this above equation we get the displacement.

r= -2cos3t i+2sin2t j+t^3+2