An object moves with velocity vector SolutionVelocity vector

Solution

Velocity vector is (cos t, sin t, t). So integrating we get (sint+c1,-cos t+c2, ( t^2/2)+c3).

Now at t=0, the position vector is at (0,0,0).

Thus, equating the the position vector obtained to (0,0,0), we get

sin 0 + c1=0, so c1=0, then -cos 0 +c2 = 0 gives, c2=1, and finally, (0^2/2)+c3=0 gives c3=0.

Thus, we have got the position vector, as r(t)= (sin t, -cos t+1, (t^2/2)).