A 2 kg particle moving along the x axis is subjected to a force F x that depends

Question

A 2 kg particle moving along the x axis is subjected to a force Fx that depends on position as shown

a) Find the acceleration of the particle at x = 4 m.( my answer is -2 m/s^2 )
(b) Find the work done by the force as the particle moves from x = 0 to x = 8.0 m. ( my answer is 6 J )

(c) Find the particle’s speed at x = 4 m if the particle starts from rest at x = 0. ( my answer is 2.5 m/s )

(d) Find the particle’s speed at x = 8 m if the particle starts from rest at x = 0. ( my answer is 5 m/s )

Explanation / Answer

a) at x = 4 m

F = 2 N

acceleration = 2/2

acceleration = 1 m/s^2

b)

work done by F = area under the F-x curve

work done by F = 0.5 * 0.8 * 0.80

work done by F = 0.32 J

c)

for the speed at x = 4

0.5 * m * v^2 = area under the curve

0.5 * 2 * v^2 = 0.5 * 2 * 2 + 2 * 2

v = 2.5 m/s

the speed is 2.5 m/s

d) at x = 8 s

0.5 * m * v^2 = area under the curve

0.5 * 2 * v^2 = 0.5 * 2 * 2 + 2 * 2 - 0.5 * 2 * 2 + 0.5 * 2 * 2

v = 2.5 m/s

the speed is 2.5 m/s

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