Chapter 6.4, Problem 33E

Work-Energy Theorem The kinetic energy KE of an object of mass $m$ moving with velocity $v$ is defined as $\text{KE}=\frac{1}{2}m{v}^2$ . If a force $f(x)$ acts on the object, moving it along the $x$ -axis from $x_1$ to $x_2$ , the Work-Energy Theorem states that the net work done is equal to the change in kinetic energy: $\frac{1}{2}m{v}_2^2-\frac{1}{2}m{v}_1^2$ , where $v_1$ is the velocity at $x_1$ and $v_2$ is the velocity at $x_2$ .

33. Suppose that when launching an 800-kg roller coaster car an electromagnetic propulsion system exerts a force of $\left(5.7x^2+1.5x\right)$ newtons on the car at a distance $x$ meters along the track. Use Exercise 31 to find the speed of the car when it has traveled 60 meters.