Question

An automobile moves under the action of a constant power supplied by its engine, it follows that
a) The driving force and velocity, both are constant
(1)
b) The driving force is constant but not the velocity
c) The velocity is constant but not the driving force
d) Both driving force as well as velocity vary​

Answer 1

Answer:

When an automobile moves under the action of a constant power supplied by its engine, both the driving force as well as its velocity varies. (Option-d)

Explanation:

In the given scenario, the power delivered by the engine is constant.

For a straight-line motion,

Work done (W) = Force (F) × Displacement (S)

⇒ W = FdS

Power (P) = $\frac{d(W)}{dt} = F\frac{dS}{dt}$ = F×$v$ [v = velocity = $\frac{dS}{dt}$]

Here, it is given that Power = constant

∴ P ≠ 0

∴ F × $v$ ≠ 0

∴ F ≠ 0, $v$ ≠ 0

Now, Force (F) = mass (m) × acceleration (a) = m × $\frac{dv}{dt}$

∵ mass is constant, therefore, acceleration of the automobile must be variable since F ≠ 0.

Furthermore,

∵ P = F × $v$ = constant,

∴ F ∝ 1/$v$

Conclusion:

Thus, the force (driving force) is variable, and since F ∝ 1/$v$, therefore, velocity is also variable in this case.

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