26. A particle moves a distance x in time t according to equation x = (t + 5)−1. The acceleration of particle is proportional to:

26. A particle moves a distance x in time t according to equation \(x = (t + 5)^{−1}\). The acceleration of  particle is proportional to:

(a)  \((velocity)^{3/2}\)

(b)  \((distance)^2\)

(c)  \((distance)^{−2}\)

(d)  \((velocity)^{2/3}\)

Answer :  (a)  \((velocity)^{3/2}\)

\(x = (t + 5)^{−1}\)

v = \(\frac{dx}{dt}\) = -1 \((t + 5)^{−2}\)

a = \(\frac{dv}{dt}\) = 2 \((t + 5)^{−3} \propto v^{3/2}\)

= 2 \(x^3\)