The acceleration of a particle is defined by the relation a= -k/x. It has been experimentally determined that v=15 ft/s when x=0.6 ft and that v=9 ft/s when x=1.2 ft. Determine (a) velocity of particle when x=1.5 ft.(b)Position of particle at which velocity is zero.

(a)  5.89 ft/s

(b) x= 1.77 ft

Explanation:

Given that the acceleration of the particle, a=-k/x

As , so

On integrating both sides, we have

where C is a constant.

At x=0.6 ft, v=15 ft/s

From equation (i)

Similarly, at x=1.2 ft, v=9 ft/s

From equation (ii),

Putting the value of k and C in the equation (i), we have

(a) At x=1.5 ft, the velocity of the particle is

ft/s

At x=1.5 ft, the velocity of the particle is 5.89 ft/s.

(b) For v=0, we have

ft

At x= 1.77 ft the velocity of the particle is zero.

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