Answer :
The work required to move the motorcycle from rest to a speed of v/4 is 1/16 times of the initial work w.
As we already know, from the work energy theorem,
That work done by all the conservative forces and all the none conservative forces on the body is equal to the change in kinetic energy of that body.
So, in formula form, it can be written as,
W = ∆K
Where w is work done on the body and ∆K is the change in kinetic energy of the body.
So, if now we assume, that the work done to increase the velocity of the body from zero to V is w, then we can write,
w = 1/2mv² ..... Equation 1
m is the mass of the body.
Now, as per the question,
Let us say the work done needed to increase the speed of the body from rest to v/4 is w', then we can write,
w' = 1/2m(v/4)² ..... Equation 2
Now,
Dividing equation 2 by 1,
We get,
w'/w = 1/16
So, the value of w' is w/16.
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