Question

If a car is moving with a velocity v, the distance the car takes to come to a halt is ___________ the distance that same car would take if it was starting with a velocity 2v.

Answer 1

one forth.

Step-by-step explanation:

car is moving at the speed of v

car stops, final speed = s

distance to stop the car = ?

using equation of motion

u_i² = u_f² + 2 a s

0² = v² - 2 a s

-ve sign is used because the car is decelerating.

`s = (v^2)/(2a)`

now, if the velocity of the car is 2v distance to stop

`s' = ((2v)^2)/(2a)`

`s' = 4(v^2)/(2a)`

`s' = 4 s`

`s = (s')/(4)`

now, the distance is one forth.

so, car with speed v has to cover one forth of the distance cover by car with speed 2 v.