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How many times more distance does it take to stop when speed is doubled?
Wiki User
∙ 12y ago
Assuming a constant, linear deceleration, it takes four times the distance to stop when you double your speed.
Using the formula v2 = u2 + 2as
where v is final speed
u is initial speed
a is acceleration
s is distance
We can rearrange the formula to solve for s giving: s = (v2 - u2)/2a
If we are finding the distance to that it takes to stop, the final velocity will be 0.
Therefore distance to stop is given by s = -u2/2a
Now we will look at the distance it takes to stop when speed is doubled. This will make our initial speed 2u.
s = -(2u)2/2a = -2u2/a
Comparing the two, we can see that when initial speed is doubled, it takes four times the distance to stop.
(While it may look strange in the formula to have a negative sign in a distance measurement, remember that the car is decelerating, giving a negative acceleration. This means that the overall expression for distance will be positive.)
Wiki User
∙ 12y ago
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