A bus starts from rest with constant acceleration of 5 `ms^–2`. At the same time a car travelling with a constant velocity of 50 `ms^–1` overtakes and passes the bus. (i) Find at what distance will the bus overtake the car ? (ii) How fast will the bus be travelling then ?

Options

A. `25 ms ^(-1)`
B. `50 ms^(-1)`
C. `75 ms^(-1)`
D. `100 ms^(-1)`

Answer

D

Explanation

Let the bus overtake the car after time t at distance s .
Using the relation , `s = ut +1/2 at^(2)`
For bus , `s = 0 +1/2 xx 5 xx t^(2) `
For car , s = 50 t , `:. 5/2 t^(2) = 50 t " or " t = 20 s`
If v is the velocity of the bus after time t , then
`v = 0+5 xx 20 = 100 ms ^(-1)`