A particle move a distance `x` in time `t` according to equation `x = (t + 5)^-1`. The acceleration of particle is alphaortional to.

Options

A. `("velocity")^(3//2)`
B. `("distance")^2`
C. `("distance")^(-2)`
D. `("velocity")^(2//3)`

Answer

A

Explanation

Distance, `x = (t+ 5)^(-1)" "..(i)`
Velocity , `v=(dx) /(dt) (t+5)^(-1)`
`=- (t+5)^(-1)" "....(ii)`
Acceleration, `a = (dv)/(dt) =(d)/(dt) [-(t+5)^(-2)]`
`=2 (t+5)-3" "..(iii)`
From equation (ii) , we get
`v^(3//2) = - (t+5)^(-3)" "..(iv)`
Substituting this in equation (iii) we get ,
Acceleration , `a = - 2v^(3//2)`
or `a prop ("velocity") ^(3//2)`
From eqution (i) , we get
`x^(3) = (t+5)^(-3)`
Substituting this in equation (iii) , we get
Acceleration , `a = 2 x^(3)`
or ` a prop " (distance )"^3`
Hence , option (a) is correct.