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.
I think I need to find the velocity equation then take the absolute value of the integral from 0 to 30, but I'm not sure how to find the velocity equation.

Answer 1

From an acceleration-time graph, you can work out the area under the graph to find the velocity. There are two triangles on the graph as shown below. The total area of the triangles are

$\frac{(10)(10)}{2}+ \frac{(20)(20)}{2}=250 ft/sec^{2}$

Hence, the distance is 250×30=7500 ft