Rectalinear Motion Question proving to be difficult

Question

A body initially at an origin, (0), and at that instant the body has a velocity of 14 m/s. The acceleration, t seconds later, is (3t-11) m/s^2. Find the velocity of the body when it is next at 0.

Answer 1

v'(t) = a(t)  so ∫a(t)dt = v(t).

 

∫(3t-11)dt = ½•3•t² -11t + C = v(t)

 

using the initial condition v(0) = 14, we get C = 14.

 

The derivative of Displacement s(t) is s'(t) and this equals the velocity, so ∫v(t)dt = s(t);

∫( ½•3•t² - 11t + 14)dt = s(t) = ½t³ - (11/2)t² +14t + K but K = 0 since s(0)= 0.

 

Now it's just a question of using the calculator to find the next value of t for which s(t) = 0.  Using whatever that t is, compute v(t) to get the requested answer.  (I leave this to you, along with the advice "CHECK MY WORK")