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Question

A curve is drawn expressing the kinetic energy of a particle as a function of the distance traversed (on X-axis). The slope of this curve represents the instantaneous:

A
velocity
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B
acceleration
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C
force
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D
power
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Solution

The correct option is C force
slope = dK/dx
total energy(E) is always constant
E = Kinetic + Potential = K + U
diffrentiating w.r.t. x we get
dE/dx = dK/dx + dU/dx
0 = dK/dx + dU/dx
slope = -dU/dx = Force (by definition)

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