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

What is the velocity of the car when t = 6? You must show your work and include units in your answer.

Answer 1

assuming the graph of acceleration is the line
a = 6mt
so,
v = 3mt^2 + c
v(0)=0, so c=0
x = mt^3 + c
x(0) = 10, so c=10, and

x(t) = mt^3 + 10

so, once you decide on m, you can figure x(6)