A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10.

Question

A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10.
What is the velocity of the car when t = 6? 
I can't show the graph, but the y intercept is at (0,10) and the x intercept is (10,0).
Can someone help me get started on this problem? Then I think I can do the rest.

Steve · Answer

Apparently a(t) = 10-t the velocity v(t) = ∫a(t) dt use v(0)=0 to determine the C introduced the position s(t) = ∫v(t) dt use s(0)=10 to determine the C introduced.