The decleration of a car travelling on astraight highway is a function of its instantaneous velocity 'v' given by `w =asqrtv`, where 'a' is a constant . If the initial velocity of the car is 60 km/hr, the distance the car will travel and the time it takes before it stops are

Options

A. 2/3m,1/2s
B. 3/2am, 1/2a s
C. 3a/2 m, a/2s
D. 2/3a m, 2/as

Answer

D

Explanation

Answer (4) `dv/dt = asqrtv`
`dv/sqrtv = adt` .
`int_vi^vf dv/sqrtv = a int dt`.
`t = 2/a v^1/2` .
since initial velocity is 60 km/hr, .
t= 2/a sec .
Deceleration(-ve) -dv/dt = `asqrtv` .
`dv/dx dx/dt = -asqrtv` .
dv/dx v = `-asqrtv` .
`dv sqrtv = -a.dx` .
x is considered as distance .
`Rightarrow dvsqrtv = -a.ds` .
`Rightarrow int_vo^0 dv sqrtv = -a intds`.
`therefore s = 2/3a v_@^3/2 m`.