SATHEE: Work Energy and Power - Result Question 37

Work Energy and Power - Result Question 37

40. A car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_{0}$ . The instantaneous velocity of this car is proportional to :

[2012M]

(a) $t^{2} P_{0}$

(b) $t^{1 / 2}$

(d) $\frac{t}{\sqrt{m}}$

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Answer:

Correct Answer: 40. (b)

Solution:

(b) Constant power of car $P_{0} = F \cdot V =$ ma.v

$P_{0} = m \frac{d v}{d t} \cdot v$

$P_{0} d t = m v d v$ Integrating

$P_{0} \cdot t = \frac{m v^{2}}{2}$

$v = \sqrt{\frac{2 P_{0} t}{m}}$

$∵ P_{0}, m$ and 2 are constant

$∴ v \propto \sqrt{t}$

At constant power, $P =$ constant

$P = F v = \frac{m d v}{d t} v = P (∵ F = \frac{m d v}{d t})$

$\Rightarrow v d v = \frac{P}{m} d t$

Integrating both sides, we get

$\begin{aligned} \int v d v = \int \frac{P}{m} t \\ (i) & \Rightarrow \frac{v^{2}}{2} = \frac{P}{m} t + C_{1} \end{aligned}$

At $t = 0, v = 0$

$∴ C_{1} = 0$

From equation (i) we get

$V^{2} = \frac{2 P t}{m} \Rightarrow V = (\frac{2 P t}{m})^{1 / 2}$

Work Energy and Power - Result Question 37

40. A car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_{0}$ . The instantaneous velocity of this car is proportional to :

Answer:

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Work Energy and Power - Result Question 37

40. A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P0. The instantaneous velocity of this car is proportional to :

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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40. A car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_{0}$ . The instantaneous velocity of this car is proportional to :