Question:
A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to :
A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to :
Show Hint
Constant power means \(Pt = \frac12 m v^2\), so \(v \propto t^{1/2}\); integrate once more to get the distance.
Updated On: Nov 4, 2026
- \(t^{\frac{3}{2}}\)
- \(t^{\frac{1}{2}}\)
- \(t^{\frac{1}{4}}\)
- \(t^{\frac{3}{4}}\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Work done by the machine in time \(t\): \(W = Pt\). Starting from rest, this equals the kinetic energy: \(Pt = \dfrac12 m v^2\).
\(v = \sqrt{\dfrac{2P}{m}}\;t^{1/2}\).
Distance: \(s = \displaystyle\int_0^t v\,dt = \sqrt{\dfrac{2P}{m}}\cdot\dfrac{2}{3}\,t^{3/2}\).
Hence \(s \propto t^{3/2}\).
Answer: (1) \(t^{3/2}\)
\(v = \sqrt{\dfrac{2P}{m}}\;t^{1/2}\).
Distance: \(s = \displaystyle\int_0^t v\,dt = \sqrt{\dfrac{2P}{m}}\cdot\dfrac{2}{3}\,t^{3/2}\).
Hence \(s \propto t^{3/2}\).
Answer: (1) \(t^{3/2}\)
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
- A particle starts with an initial velocity of 10.0 m/s along x-direction and accelerates uniformly at the rate of 2.0 m/s$^2$. The time taken by the particle to reach the velocity of 60.0 m/s is
View More Questions
Top JEE Main work, energy and power Questions
- A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be:
- A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force exerted by the ball on the hand of the player is:
- A bag of sand of mass $98\, kg$ is suspended by a rope A bullet of $200\, g$ travelling with speed $10\, ms ^{-1}$ gets embedded in it, then loss of kinetic energy will be
- A spherical body of mass $2\, kg$ starting from rest acquires a kinetic energy of $10000\, J$ at the end of $5^{\text {th }}$ second The force acted on the body is ___$N$
View More Questions
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
View More Questions