A 286-kg motorcycle is accelerating up along a ramp that is inclined 31.6° above the horizontal. The propulsion force pushing the motorcycle up the ramp is 3168 N, and air resistance produces a force of 230 N that opposes the motion. Find the magnitude of the motorcycle's acceleration.

The acceleration motorcycle

a = 5.13 m / s²

Explanation:

Now to determine the acceleration of the motorcycle

Use the force to analysis motion

∑ F = m * a

∑ F = E - D - m*g * sin (β) = m * a

E = 3168 N

D = 230 N

β = 31.6 °

3168 N - 230 N - 286 kg * 9.8 m / s² * sin (31.6°) = 286 kg * a

Now solve to a'

a = [ 3168 N - 230 N - 286 kg * 9.8 m / s² * sin (31.6°) ] / (286 kg)

a = 5.13 m / s²