A car accelerates from rest with `2 m // s^(2)` on a straight line path and then comes to rest after applying brakes. Total distance travelled by the car is 100 m in 20 seconds. Then, the maximum velocity attained by the car is

Options

A. 10 m/s
B. 20 m/s
C. 15 m/s
D. 5 m/s

Answer

a

Explanation

Given
Acceleration of car `(alpha) = 2 m//s^(2)`
Distance covered by car in 20 second (s) = 100
we know that,
`s = (1)/(2). (alpha beta)/(alpha + beta) t^(2)`
`100 + (1)/(2) xx (2 beta)/((2 + beta)) xx 20 xx 20`
`(100)/(200) = (beta)/((2 + beta))`
`implies (1)/(4) = (beta)/(2 + beta)`
`implies 4 beta = 2 + beta`
`implies 3 beta = 2 implies` retardation `beta = (2)/(3) m//s^(2)`
`:.` Maximum velocity `(V_("max")) =(alpha beta t)/(alpha + beta)`
`= (2 xx (2)/(3) xx 20)/(2 + (2)/(3)) = ((80)/(3))/((8)/(3)) = (80)/(3) xx (3)/(8)`
= 10 m/s