# Thread: [SOLVED] Potential energy and conservative force?

1. ## [SOLVED] Potential energy and conservative force?

The potential energy of a particle of mass 5 kg, moving in the xy plane is given by U = -7 x + 24 y J, x and y being in metres. Initially(at t = 0), the particle is at the origin and has velocity v = (14.4i + 4.2j) m/s. Then(let only conservative force be present),

A) Speed of the particle at t = 4 s, is 25m/s
B) the acceleration of the particle is 5m/s^2
C) the direction of acceleration of the particle is perpendicular to its direction of motion, initially
D) the direction of acceleration of the particle is along the direction of motion initally.

More than one options may be correct.

2. Originally Posted by fardeen_gen
The potential energy of a particle of mass 5 kg, moving in the xy plane is given by U = -7 x + 24 y J, x and y being in metres. Initially(at t = 0), the particle is at the origin and has velocity v = (14.4i + 4.2j) m/s. Then(let only conservative force be present),

A) Speed of the particle at t = 4 s, is 25m/s
B) the acceleration of the particle is 5m/s^2
C) the direction of acceleration of the particle is perpendicular to its direction of motion, initially
D) the direction of acceleration of the particle is along the direction of motion initally.

More than one options may be correct.
Note that $F = - \nabla U \Rightarrow a = - \frac{\nabla U}{5}$.

3. Is that the del operator?(as in d/dr r)?

I tried this:

F = -(∂/∂x U i + ∂/∂y U j)
= -(-7i + 24j)
= 7i - 24j

Am I correct?

4. Originally Posted by fardeen_gen
Is that the del operator?(as in d/dr r)?

I tried this:

F = -(∂/∂x U i + ∂/∂y U j)
= -(-7i + 24j)
= 7i - 24j

Am I correct?
Yes.