The same power P is delivered to two systems over times and , respectively. As a result of power delivered the object accelerates. If , what is the ratio of the times, ?
A) 0.25
B) 4
C) 16
D) 0.0625
E) 1

Question

Quizplus · Accepted Answer

The work done on an object is given by the formula 
W = F*d = m*a*d 
where F is the force applied, d is the distance over which the force is applied, m is the mass of the object, a is the acceleration produced and W is the work done.

Now, the power delivered is simply the rate at which work is done: 
P = W/t
where t is the time taken to do the work.

We are given that the same power P is delivered to both systems, so we can write:
P = W/t1 = W/t2

Let's assume that the mass of the object is the same in both systems (we can do this since the problem doesn't tell us otherwise). 
Then we have:

m*a1*d = P*t1 
and 
m*a2*d = P*t2

Dividing these two equations, we get:

a1/a2 = t2/t1

But we are given that a1 = 4*a2, so we can substitute that in above equation to get:

4 = t2/t1

Hence, t2/t1 = 4, or t2 = 4*t1.

Therefore, the ratio of the times t2/t1 is 4:1, or 16:4, or 0.25:1. This reduces to the simplest form of 1:4.

So the answer is C.

The Same Power P Is Delivered to Two Systems Over