Question

A particle of mass m is driven by a machine that delivers a constant power k watt.
If the particle starts from rest the force on the particle at time t is
A. $$\sqrt{mk}{t}^{-1/2}$$
B. $$\sqrt{2mk}{t}^{-1/2}$$
C. $${\displaystyle \frac{1}{2}}\sqrt{mk}{t}^{-1/2}$$
D. $$\sqrt{{\displaystyle \frac{mk}{2}}{t}^{-1/2}}$$

Answer 1

Hint: A unit of power is proportionate to a unit of work separated by a unit of time. In this way, a Watt is comparable to a Joule/second. Thus, power of a machine is the work/time proportion for that specific machine.

Complete step-by-step answer:
The correct answer is D.
$${\displaystyle \frac{dW}{dt}}=P$$
$$\Rightarrow W=Pt$$
$$\Rightarrow {\displaystyle \frac{1}{2}}m(v_2^2-v_1^2)=Pt$$
$${\displaystyle \frac{1}{2}}m{v}^2=Pt$$
$$v=\sqrt{{\displaystyle \frac{2Pt}{m}}}$$
$$a={\displaystyle \frac{dv}{dt}}=\sqrt{{\displaystyle \frac{2P}{m}}}{\displaystyle \frac{1}{2}}{t}^{-1/2}$$
$$F=ma=$$$$\sqrt{{\displaystyle \frac{mk}{2}}{t}^{-1/2}}$$
Energy is the capacity to perform Work. Energy can nor be made nor devastated. It must be changed starting with one kind then onto the next. The unit of Energy is the same as of Work, for example, Joules. Energy is found in numerous things, and along these lines, there are various sorts of Energy.

All types of Energy are either kinetic or potential. The Energy in motion is known as Kinetic Energy while Potential Energy is the Energy put away in an object and is estimated by the measure of Work done.

Energy is the capacity to perform Work. Energy can nor be made nor obliterated. It must be changed starting with one kind then onto the next. The unit of Energy is the same as of Work, for example, Joules. Energy is found in numerous things, and in this manner, there are various sorts of Energy.

All types of Energy are either kinetic or potential. The Energy in motion is known as Kinetic Energy through Potential Energy is the Energy put away in an object and is estimated by the measure of Work done.

Note: As power doesn't have any course, it is a scalar amount. The SI unit of power is Joules every Second (J/s), which is named as Watt. Watt can be characterized as the power taken to do one joule of Work in one second. The unit Watt is devoted out of appreciation for James Watt, the engineer of the steam motor.