Question

at t=0, a particle starts at the origin with a velocity of 6ft persecond and moves along the x-axis in such a way that at time t its acceleration is 12t^2 ft per second per second. through how many feet does the particle move during the first 2 seconds?

Answer 1

Traveled distance \(x=v_0t+\frac{1}{2}at^2\). Plug \(v_0=6\), \(a=12(2)^2\) and \(t=2\), and then solve for x.