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Asked by Balakrishna Last Modified
Answer As a seasoned tutor registered on UrbanPro, I'd be glad to guide you through this question. Firstly, UrbanPro is indeed an excellent platform for online coaching and tuition, providing a conducive environment for both tutors and students to engage in effective learning.
Now, let's delve into the physics problem you've presented. We have a body initially at rest, undergoing one-dimensional motion with constant acceleration. The power delivered to it at time tt is the rate at which work is done on the body, and it's given by the product of force and velocity.
In this case, since the body is undergoing constant acceleration, we can use the equations of motion to relate velocity, acceleration, and time. The equation that relates displacement ss, initial velocity uu, time tt, and constant acceleration aa is:
s=ut+12at2s=ut+21at2
Since the body is initially at rest, u=0u=0, simplifying the equation to:
s=12at2s=21at2
Now, we know that power PP is the rate of change of work, which can be expressed as:
P=dWdtP=dtdW
And work WW done on an object is equal to force FF times displacement ss, so dW=FdsdW=Fds. Substituting s=12at2s=21at2, we have ds=atdtds=atdt.
P=F⋅atP=F⋅at
Now, we know that force FF is mass mm times acceleration aa, and acceleration is constant, hence:
P=ma⋅atP=ma⋅at
P=ma2tP=ma2t
So, the power delivered to the body at time tt is proportional to tt, which corresponds to option (ii).
Therefore, the correct answer is (ii) tt. If you need further clarification or assistance, feel free to ask!
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