Question

Q. Position of the particle varies with time as x ∝ t½. Find the relation between velocity and acceleration.

Answer 1

Answer:

Relation is v = -2at

Explanation:

x ∝ t½

x = k $\sqrt{t}$

∴ v = dx/dt = k {1/2$\sqrt{t}$}   . . . . . (1)

   a = d²x/dt² = k/2[-1/2 $t^{-3/2}$] = - k/(4$t^{3/2}$)    . . . .(2)

(1)/ (2)

v/a =  - 4$t^{3/2}$ / 2$t^{1/2}$

     = -2 t

∴ v = -2at