A 2.0-kg object is moving without friction along the x-axis.The potential energy curve as a function of position is shown in the figure,and the system is conservative.If the speed of the object at the origin is 4.0 m/s,what will be its speed at 7.0 m along the +x-axis?
A) 4.0 m/s
B) 4.2 m/s
C) 4.4 m/s
D) 4.6 m/s
E) 9.8 m/s

Question

A 2.0-kg object is moving without friction along the x-axis.The potential energy curve as a function of position is shown in the figure,and the system is conservative.If the speed of the object at the origin is 4.0 m/s,what will be its speed at 7.0 m along the +x-axis? 
A) 4.0 m/s 
B) 4.2 m/s 
C) 4.4 m/s 
D) 4.6 m/s 
E) 9.8 m/s

Quizplus · Accepted Answer

Conservation of mechanical energy gives us:
K1 + U1 = K2 + U2
where K1 = (1/2)mv1^2, U1 is the gravitational potential energy at the origin, K2 = (1/2)mv2^2, and U2 is the gravitational potential energy at x = 7.
At the origin, U1 = 0 since the reference level is set at x = 0.
At x = 7, U2 = -10 J
Thus,  (1/2)mv1^2 = (1/2)mv2^2 - 10 J
Simplifying and solving for v2:
v2 = sqrt(v1^2 + 20/m)
Plugging in the given values, we get:
v2 = sqrt(4^2 + 20/2) = 4.2 m/s
Therefore, the answer is B.

A 20-Kg Object Is Moving Without Friction Along the X-Axis