# W=F.dx rate of change of x approaches to zero?

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1. Oct 21, 2014

### hugoARD

In the integration of Force with respect to displacement (W=∫F.dx), is that true if the rate of change of displacement approaches to zero? My teacher said the one which approaches to zero is the rate of change of time. But If I arrange the formula, I will get F=dW/dx then F= lim Δx→0 ΔW/Δx. Please help

2. Oct 21, 2014

### Staff: Mentor

Hi hugoARD. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

I think you may have misunderstood your teacher, time plays no part in that equation for work. The time rate of change of x is immaterial, though obviously if dx/dt is fixed at zero then x undergoes no change and with no change in x then no work is done.

You perform exactly as much work over a distance x whether your movement over that distance is fast or slow, providing you push with the same force.

Last edited by a moderator: May 7, 2017
3. Oct 21, 2014

### Staff: Mentor

Rate of change of displacement with respect to what?

That makes sense. If the rate of change of displacement with respect to time goes to zero, that means the velocity goes to zero and the rate at which work is done goes to zero: dW/dt = F dx/dt

dW/dx describes how work changes with distance. It equals force, not zero.