The velocity of a particle at time t is : vextor V = ti + t^2k if at time t = 0 , the particle is at origin, find its position vector

Answer 1

Velocity is the derivative of position with respect to time.

Let's call position vector r (don't want to use x because it is in x and z directions) so v = dr/dt

You can rewrite v = dr/dt as vdt = dr and then integrate both sides: ∫dr = ∫vdt

Let's substitute your function of velocity in to the integral: ∫dr = ∫(t i + t² k) dt (remember i and k are just directions for the vector.)

r = 1/2t² i + 1/3t³ k + C For t = 0, the particle is at 0i and 0k - this helps us solve for the constant.

0 = 1/2(0)² i + 1/3(0)³ k + C so C = 0.