Question

The acceleration of an object is given by the equation a(t) = 8, where a is in m/s2 and t is in seconds. The object is initially at rest at the origin. A constant force of 11 N acts on the object. What is the power delivered to the object at t = 5 s? 470 W 410. W 500. W 440. W 540. W

Answer 1

Using the symbols for velocity, for displacement.

Given:-

• ​​​​​​​An object initially at origin at rest. Therefore $s=0$ and $v=0$ at $t=0$ .
• Acceleration of the object, $a=8m/s^{2}$ .
• A constant force acting on the object,
  F = 11N
  .

Now we have to find the power delivered to the object at $t=5s$ .

• Power is the rate of change in Energy with respect to time, mathematically $P=\frac{dE}{dt}$ .
• Now if we get to know the energy, of the object as a function of time, we can easily calculate the power, using the above relation.

Now we can apply the following simple kinematic equation on the object:-

• $v=u+at$

As $u=0$ , applying this equation we get:-

• $v=8t$

As $a=8m/s^{2}$ and
F = 11N
, using
F=ma
, we get

• $m=\frac{11}{8}kg$

Object has only kinetic energy, therefore $E=\frac{1}{2}mv^{2}$ .

• $E=\frac{1}{2}mv^{2}=\frac{1}{2}\frac{11}{8}(8t)^{2}=44t^{2}$
• $P=\frac{dE}{dt}=\frac{d(44t^{2})}{dt}=88t$​​​​​​​

Therefore, at $t=5s$ ,

$P=88t=88*5=440W$

Correct answer is .

Another approach:-

• Energy supplied to the object = Work done on the object.
• Work done, $W=F.s$
• $P=\frac{dE}{dt}=\frac{dW}{dt}=\frac{d(F.s)}{dt}$
• As $F=constant$ , $P=F\frac{ds}{dt}=Fv$ ​​​​​​​

At $t=5s$ , $v=8t=8*5=40m/s$

Therefore,

​​​​​​​$P=Fv=11*40=440W$.