An auto travelling along a straight road increases its speed from `30.0 m s^(-1)` to `50.0 m s^(-1)` in a distance of 180 m. If the acceleration is constant, how much time elapse while the auto moves this distance?

Options

A. 6.0 s
B. 4.5 s
C. 3.6 s
D. 7.0 s

Answer

B

Explanation

Let a be constant acceleration of auto. Here, u = `30 m s^(-1), v = 50 m s^(-1)`, S = 180 m
As `v^(2) - u^(2) = 2aS`
`(50)^(2) - (30)^(2) = 2 xx a xx 180` therefore `a = 1600/2 xx 180 = 40/9 m s^(-2)`
As `S = ut + 1/2 at^(2) implies 180 = 30 xx t + 1/2 xx 40/9 xx t^(2)`
`implies 2t^(2) + 27t - 162 = 0`
Solving this quadratic equation by quadratic formula, we get `= 4.5 s, -18` s, (t can't be negative) `therefore` t = 4.5 s