Find the position function from the given velocity function and initial value. Assume that units are feet and seconds.

Question

Find the position function  from the given velocity function and initial value. Assume that units are feet and seconds.

Quizplus · Accepted Answer

We know that position is the integral of velocity with respect to time. 
So, integrating the given velocity function, we get
position = ∫(4t+5)dt = 2t^2 + 5t + C
where C is the constant of integration. 
We can find the value of C using the initial value given.
When t=0, position=3. So,
3 = 2(0)^2 + 5(0) + C
C = 3
Therefore, the position function is given by
position = 2t^2 + 5t + 3, which is option A.

Find the Position Function from the Given Velocity Function