### Home > APCALC > Chapter 7 > Lesson 7.1.5 > Problem7-51

7-51.

The point from problem 7-19 travels along the x-axis so that at time t its position is given by $s(t) = t^3 - 5t^2 + 4t$, where $0 ≤ t ≤ 5$. Calculate the average velocity of the point. At what time(s) during the interval was the point traveling at this average velocity? Homework Help ✎

This is an application of the Mean Value Theorem of $f(x)$ (given $F(x)$).
In other words, where on the interval $[0,5]$is the slope of the tangent the same as the slope of the secant?

Determine where IROC = AROC.

$v(t)=s'(t)=3t^{2}-10t+4=\frac{s(5)-s(0)}{5-0}$

real velocity = average velocity
slope of tangent = slope of secant
Solve for $t$ to find out WHERE the equation above holds true.