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Question

A particle of mass m is at rest at the origin at time t=0. It is subjected to a force F(t)=F0ebt in the x-direction .Its speed v(t) is depicted by which of the following curves ?
 


Solution

The correct option is B
We will try to solve this question by using some common sense.
F=F0ebt will always be a positive quantity as exponential function always remains positve.
It means that the acceleration will always remain in positive x- direction.

If the acceleration is in +ve x- direction and the body is starting from rest then the velocity will also be in +ve x-direction.
The velocity will keep increasing as there is no reason for the velocity to change its direction . So, the velocity will keep increasing in +ve x-direction.

From this we can easily eliminate options (a) and (d)
Now the only difference that lies between option (c) and (d) is its peak value on the graph.
We can compare them by dimensional analysis
F=F0ebt Here F and F0 both are forces which means ebt is an dimensionless quantity.
b=1t
and its unit is sec1
This means that F0bm is dimensionally incorrect.
Option B is correct
 

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