The engine of a motoecycle can produce a maximum acceleration of `5 m//s^(2)`. Its brakes can produce a maximum retardation of `10 m//s^(2)`. What is the minimum time in which the motorcycle can cover a distance of `1.5 km`?

Options

A. 30sec
B. 15sec
C. 10sec
D. 5sec

Answer

A

Explanation

During acceleration –
`t_1 = (v_(max))/(alpha)`

During retardation
`t_2 = (v_(max))/(beta)`
`t_1 + t_2 = t`
`v_(max) = (alpha beta t)/(alpha + beta)`
Average acceleration ` = (alpha beta)/(alpha + beta)`
Distance (s) ` = 1/2 ((alpha beta)/(alpha + beta)) t^2`
`rArr 1500 = 1/2 ((5 xx 10)/(15))t^2`
`t = sqrt((2 xx 15 xx 1500)/(5 xx 10)) = 30sec`