Prove that the given relation and explain the difference between given derivatives.
The given relation is , where
The given derivatives are and .
Acceleration is the rate of change of velocity with respect to time.
For increasing velocity, the sign of will be positive and for the decreasing velocity, the sign of will be negative.
Divide both sides by .
Apply chain rule.
is the rate of change of the velocity with respect to displacement.
Whenthe displacement increases, the velocity is increasing, when the displacement decreases, the velocity is decreasing.
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