Suppose that your car ran out of gas. So you (1) push your car a distance of 200

Question

Suppose that your car ran out of gas. So you (1) push your car a distance of 200 m on a level road to the gas station, which takes you 10 minutes. (2) If you could have pushed your car with the same force across the same distance but over a longer time period (20 minutes), then

A) you would have done more work for scenario (2) than scenario (1).

B) you would have done less work for scenario (2) than scenario (1).

C) the power associated with scenario (2) is less than for scenario (1).

D) the power associated with scenario (2) is greater than for scenario (1). E) the potential energy increases when you push the car this distance

Explanation / Answer

Workdone is given by:

W = F.d = F*d*cos A

Since force is in direction of displacement so A = 0 deg

cos A = cos 0 = 1

W = F*d

Now since in both case force and distance is same, So workdone in both scenario will be equal

W1 = W2

Now power is given by:

Power = Workdone/time

So we can see that power is inversely proportional to time, if the workdone is constant,

Since time in scenario 2 is greater than scenario 1, So power is scenarion 2 will be less for scenario 1.

Since t2 > t1, So P2 < P1, (due to inversible proportionality)

Which means correct option is C.

Also potential energy is given by: PE = m*g*(h1 - h2)

h1 - h2 = 0, Since flat surface, So PE1 = PE2, which means there will be no increase in PE.

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