Question

A 150 g particle at x = 0 is moving at 8.00 m/s in the +x-direction. As it moves, it experiences a force given by Fx=(0.850N)sin(x/2.00m). What is the particle (s) speed when it reaches x = 3.14 m?

Answer 1

To find the speed of the particle at x = 3.14 m, we need to integrate the force function and use the work-energy theorem. The particle's speed is approximately 3.27 m/s.

Step-by-step explanation:

To find the speed of the particle at x = 3.14 m, we need to integrate the force function over the range of x from 0 to 3.14.

First, let's calculate the work done by the force:

W = ∫Fx dx = ∫ (0.850N)sin(x/2.00m) dx

Integrating this expression, we find that the work done is approximately 1.628 Joules.

To find the particle's speed, we can use the work-energy theorem:

K = W

(1/2)mv2 = 1.628

Solving for v, we find that the particle's speed is approximately 3.27 m/s.