# Energy and Speed

1. Apr 5, 2005

### Honore

With reference to the attached "energy versus distance graph" of two particles;

a. What minimum speed (m/s) does a 100 g particle need at point A to reach point B?

b. What minimum speed (m/s) does a 100 g particle need at point B to reach point A?

Thank you.

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2. Apr 5, 2005

### Galileo

Use conservation of energy. First find the minimum kinetic energy needed to go from A to B, then get the speed from that.

3. Apr 5, 2005

### Honore

In order to find the minimum kinetic energy, I think I have to find the total work done referring to a "Force vs Distance" graph. But, how can "Force" be found from a graph which is not linear?

4. Apr 5, 2005

### whozum

Work = $\int F dx$

Is this gravitational potential? In that case, its conservative, and you can ignore anything but the starting and ending points. You lost 2 Joules of PE to get from A to B, so you gained 2 Joules of KE.

$$KE = 1/2 mv^2$$

$$2 = 1/2 (100g) v^2$$

5. Apr 5, 2005

### Galileo

In one dimension, any position dependent force is conservative (the potential (or total?) energy is already given as a function of the position).

6. Apr 5, 2005

### whozum

Isnt "position dependant force" part of the definition of "conservative force"? Say there was a resistance factor such as friction, the energy wouldn't be conserved then.

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