The braking distance is given by [tex]s=\frac{-u^2}{2a}[/tex]
Explanation:
When the driver of a car hits the pedal of the brakes, the car starts decelerating until it stops. Assuming the deceleration is constant, then the motion is a uniformly accelerated motion, so we can use the following suvat equation:
[tex]v^2-u^2=2as[/tex]
where
u is the initial speed of the car
v is the final speed of the car, which is zero because the car comes to rest:
v = 0
a is the acceleration of the car
s is the distance travelled by the car during the deceleration, so it is the braking distance
Therefore, re-arranging the equation for s, we find an expression for the braking distance:
[tex]s=\frac{-u^2}{2a}[/tex]
Note that the sign of [tex]a[/tex] is negative since the car is decelerating, therefore the final sign of [tex]s[/tex] is positive.
Learn more about accelerated motion:
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