calc question

Question

Given the following velocity function of an object moving along a line, find the position function with the initial position s(0)=0. Then, graph both the velocity and position functions.
v(t)=8t+3

 

The position function is s(t)=__

 

what would the velocity function and position function look like graphed?

Answer 1

v(t) = 8t + 3

 

s(t) = 8t²/2 + 3t + C = 4t² + 3t + C

 

s(0) = 0 ⇒ C = 0

 

s(t) = 4t² + 3t

Answer 2

v(t)  =  s'(t) = 8t + 3

 

s(t) = 4t² + 6t + C

 

since s(0) = 0, C = ) and s(t) = 4t² + 6t