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?
the graph has a y intercept of 10 and an x intercept of 10.

Answer 1

the acceleration graph is apparently

a(t) = 10-t
so, that gives us

v(t) = 10t - t^2/2 + C
v(0)=0, so C=0

so, now we have
s(t) = 5t^2 - t^3/6 + C
s(0) = 10, so C = 10

s(t) = 10 + 5t^2 - t^3/6
s(30) = 0
So, the final position is 10 ft behind the starting line.

However, the total distance traveled is
∫[0,30] |10t - t^2/2| dt = 4000/3 + 20 ft

Answer 2

So the total would be 1353.333 feet?

Answer 3

WHy would you add 20 ft

Answer 4

who knows bruh

Answer 5

There's no extra 20 XD