Question

The velocity function, in feet per second, is given for a particle moving along a straight line.
v(t) = t^3 − 9t^2 + 20t − 12, 1 ≤ t ≤ 7
Find the total distance that the particle travels over the given interval.

Answer 1

Distance is integral of velocity because velocity is the derivative of distance over time:
$$
d=\int_1^7v(t)dt=\int_1^7\left (t^3 − 9t^2 + 20t − 12\right )~dt
$$
Can you evaluate this integral?

Answer 2

yesssss I did I don't know why my answer is wrong

Answer 3

that will give you displacement

think about something like: \(\int_{1}^{7}|v(t)|dt\)

Answer 4

yes then it changes at (t-1) (t-2) (t-6)

Answer 5

it's in the interval \(1 ≤ t ≤ 7\)

so the \(2 \le t \le 6\) is the bit that needs to be thought about