calculus help needed thanks

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 total distance the car travels in this 30 second interval? Your must show your work but you may use your calculator to evaluate. Give 3 decimal places in your answer and include units.

Answer 1

All of the movement is in the positive direction, so distance = displacement. The displacement is the area under a v-t graph (or the integral of vdt for the time interval)

In this case, the area is a triangle with base Δt = 30s and height a in ft/s² times 30s (d = 1/2at²)

The initial position is irrelevant.