The acceleration a(t) of a body moving in a straight line is a (t)=8-6t. If the velocity of the body is 25 at t=1 and if s(t) is the distance of the body from the origin at time t, what is s(4)-s(2)?
1 Answer
The distance travelled between the seconds 2 and 4 is 28m.
Explanation:
The acceleration at any time is modelled by
First we have to determine the velocity at all times, we can start doing this by integrating the acceleration to get velocity.
The constant c can be found using the given information that
So
Distance can be found by integrating the velocity function. Knowing that we are trying to find the distance travelled between 2 and 4 seconds we can use a definite integral of the velocity function to find distance.
The distance travelled between the seconds 2 and 4 is 28m.