Question

A 15.00 kg particle starts from the origin at time zero. Its velocity as a function of time is given by = 8t2î + 5tĵ where is in meters per second and t is in seconds. (Use the following as necessary: t.) (a) Find its position as a function of time.

Answer 1

Answer:

Explanation:

I will assume the equation reads:

v = 8t²î + 5tĵ

The velocity v is the time derivative of the position x.

$x = \int\limits^t_0 {v} \, dt = \int\limits^t_0 {8t^{2}\hat i + 5t\hat j} \, dt = \frac{8}{3} t^{3} \hat i + \frac{5}{2}t^{2}\hat j |^t_0 = \frac{8}{3} t^{3} \hat i + \frac{5}{2}t^{2}\hat j - \frac{8}{3} \hat i - \frac{5}{2} \hat j\\ x = \frac{8}{3} (t^{3} - 1 )\hat i + \frac{5}{2} (t^{2} - 1 )\hat j$