contestada

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.

Respuesta :

Answer:

one forth.

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.

[tex]s = \dfrac{v^2}{2a}[/tex]

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

[tex]s' = \dfrac{(2v)^2}{2a}[/tex]

[tex]s' = 4\dfrac{v^2}{2a}[/tex]

[tex]s' = 4 s[/tex]

[tex]s = \dfrac{s'}{4}[/tex]

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.

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