Question
A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to :
(a) $t^{1 / 2}$
(b) $t$
(c) $t^{3 / 2}$
(d) $t^2$.

Answer

Let mass of body = m
Constant acceleration of body = a
Initial velocity u = 0 
Velocity at time t = v 
From first equation of motion
$
\begin{array}{l}
v=u+a t \\
v=0+a t=a t
\end{array}
$
Force $F =m a$ (constant)
$
\begin{aligned}
\therefore \quad \text { Power } P & =\text { F.v. } \\
& =m a \cdot a t=m a^2 t \\
P & \propto t
\end{aligned}
$
Hence, correct answer is (b).

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

For the determination of ‘g’ using a simple pendulum, measurements of I and T are required. Error in the measurement of which of these will have larger effect on the value of 'g' thus obtained and why? What is done to minimize this error?
Find the maximum wavelength of electromagnetic radiation which can create a hole-electron pair in germanium. The band gap in germanium is 0.65eV.
The contact angle between pure water and pure silver is 90º. If a capillary tube made of silver is dipped at one end in pure water, will the water rise in the capillary?
A piano wire weighing 6.00g and having a length of, 90.0cm emits a fundamental frequency corresponding to the "Middle C" (v = 261.63Hz). Find the tension in the wire.
A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observation and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of hair?
Can there be two vectors where the resultant is equal to either of them?
By evaluating $\int\text{i}^2\text{Rdt},$ show that when a capacitor is charged by connecting it to a battery through a resistor, the energy dissipated as heat equals the energy stored in the capacitor.
The temperature and the dew point in an open room are 20°C and 10°C. If the room temperature drops to 15°C, what will be the new dew point?
50m3 of saturated vapour is cooled down from 30°C to 20°C. Find the mass of the water condensed. The absolute humidity of saturated water vapour is 30gm-3 at 30°C and 16gm-3 at 20°C.
Figures(a) and (b) refer to the steady flow of a (non viscous) liquid. Which of the two figures is incorrect? Why?