The v - s graph of a gas particle moving in a straight line path in front of a table fan is as shown, where v is the velocity and s is the displacement of the particle from the table fan. Find its maximum acceleration .(Approximate to two decimal points ).

a) 3.62 m / s2 .
b) 1.62 m / s2 .
c) -1.62m / s2 .
d) - 3.62m / s2 .

 

 

The acceleration at any instant is given by velocity times slope of v - s graph.

The extremities in the acceleration occur at displacements where the differential of the acceleration equals zero.

The maximum acceleration occurs at the displacement , s, where the second differential of acceleration ( with respect to s in this case ) is less than zero.

The above equation is true for s = 2.71 m
Hence the maximum acceleration occurs when the displacement is 2.71 meters and is equal to
   a max = 3.62 m / s2 .