Question

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

• A. ${(\text{velocity})}^{3/2}$
• B. ${(distance)}^2$
• C. ${(distance)}^{-2}$
• D. ${(velocity)}^{2/3}$

Answer 1

Answer: (A)

Given, distance $x={(t+5)}^{-1}$ ?(i) Differentiating Eq. (i) w.r.t. t, we get $\frac{dx}{dt}=(v)=\frac{-1}{{(t+5)}^2}$ ?(ii) Again, differentiating Eq. (i) w.r.t. t, we get $\frac{d^{2}x}{d{t}^2}=(a)=\frac{2}{{(t+5)}^3}$ ?(iii) Comparing Eqs. (ii) and (iii), we get $a\propto {(v)}^{3/2}$