Finding velocities in F vs x graph

[mandy9008]

Homework Statement

A object of mass 3.00 kg is subject to a force Fx that varies with position as in the figure below.

Find the work done by the force on the object as it moves as follows:
(a) from x = 0 to x = 4.00 m
(b) from x = 5.00 m to x = 10.0 m
(c) from x = 11.0 m to x = 15.0 m.
(d) If the object has a speed of 0.500 m/s at x = 0, find:
speed at x = 5.00 m
speed at x = 15.0 m

The Attempt at a Solution

a. W=2.5N (4m) / 2 = 5J
b. W=3N (5m) = 15J
c. W=2.5N (4m) / 2 = 5J
d. W=1/2 mv² - 1/2 mvo²

x=5m 15J = 3kg v - (3kg)(0.500m/s)
v=2.29 m/s

x=15m 0=3kg v - (3kg)(0.500m/s)
v=0.5 m/s

 

[kuruman]

The Attempt at a Solution

a. W=2.5N (4m) / 2 = 5J

I would not use 2.5 N for the force. I suggest that you find an equation for the straight line in the form F = mx and calculate the force at 5 m.

b. W=3N (5m) = 15J

Looks good.

c. W=2.5N (4m) / 2 = 5J

Same comment as part (a)

d. W=1/2 mv² - 1/2 mvo²

x=5m 15J = 3kg v - (3kg)(0.500m/s)
v=2.29 m/s

x=15m 0=3kg v - (3kg)(0.500m/s)
v=0.5 m/s

What happened to the 1/2 and the square of the speed in the expressions above?