Question

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P. The instantaneous velocity of this car is proportional to
(1)t^2P
(2)t^1/2
(3)t^-1/2
(4)t/m^1/2

Answer 1

Answer on Question #49238-Physics-Mechanics-Kinematics-Dynamics

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P. The instantaneous velocity of this car is proportional to

(1) $t^2 P$

(2) $t^{\frac{1}{2}}$

(3) $t^{-\frac{1}{2}}$

(4) $\frac{t}{m^2}$

Solution

$$\begin{aligned} P &= F v = \left( m \frac{d v}{d t} \right) v = m v \frac{d v}{d t} \\ &\quad \int P \, dt = \int m v \, dv \\ &\quad P t = \frac{m v^2}{2} \to v = \sqrt{\frac{2 P t}{m}} \\ &\quad \therefore v \propto t^{\frac{1}{2}} \end{aligned}$$

Answer: (2) $t^{\frac{1}{2}}$.

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