A particle moves such that its velocity at time t is given by

Question

v =5t^5i + 4t^5j + t^3k.

If its position x at time t = 0 is given by x ( 0 ) = i + 2j, what is the position of the particle at time t?

Answer 1

x=INT v(t)dt
=5/6*t^6 i + 4/6 t^6 j + 1/4*t^4k+C

given t=0 x=i+2J
i+2j=i(5/6(0)+2/3 (0)j+Ok+C

C=i+2j