Question

"What is the velocity of a 2.90-kg body at x = 2.25 m if the only force acting on it along the positive x-axis has an x-component Fx = -4.40x N (with x in meters), and its velocity at x = 6.62 m is 7.23 m/s?"

Answer 1

The velocity of the 2.90-kg body at x = 2.25 m is 3.16 m/s.

Step-by-step explanation:

To find the velocity of a body at a specific position, we need to integrate the force felt by the body with respect to displacement. In this case, the force function is given as F(x) = -4.40x N. We can integrate this force from x = 6.62 m to x = 2.25 m to find the change in potential energy. Since the body is acted on by the only force along the positive x-axis, the change in potential energy is equal to the change in kinetic energy. Therefore, we can equate the final kinetic energy at x = 2.25 m to the initial kinetic energy at x = 6.62 m to solve for the velocity at x = 2.25 m.

Using K(x) = 0.5mv^2 where m is the mass and v is the velocity, we can set up the equation:

0.5 * 2.9 * v^2 = 0.5 * 2.9 * 7.23^2

Simplifying, we find that v = 3.16 m/s.