please help with this question

Question

A particle with an initial position vector r = 5i + 6j + k m has an acceleration imposed on it, given as a = 6ti + 5t^2j + 10k m/s2. If the particle has a zero velocity initially, what are the acceleration, velocity, and position of the Particle when.t = 10s

Answer 1

Velocity of particle v = ∫adt = ∫(6ti + 5t^2j + 10k)dt = 3t²i + 5t³/3j + 10tk +C, at t =0 v = 0; 0 = C,

So, v = 3t²i + 5t³/3j + 10tk. Position vector r = ∫(3t²i + 5t³/3j + 10tk)dt = t³i + 5t⁴/12j + 5t²k + C;

at t = 0 r = C = 5i + 6j + k. So, r = (t³ + 5)i + (5t⁴/12 + 6)j + (5t² + 1)k.

At t = 10 s a = (60i+ 500j + 10k) m/s²; v = (300i + 5000/3j + 100k) m/s; r = (1005i + 12518/3j + 501k) m