Ok math geniuses! If you drive twice as fast, will your stopping distance increase by.........?

Question

a) Two times
b) Three times
c) Four times
d) Five times

Answer 1

c.
e = 1/2 m v^2
if you double velocity, e increases by a factor of four

guy below me you're a complete retard.
"this is math not physics"
what exactly do you think physics is?

Answer 2

Since your tires are limited by a certain amount of grip, there is a limit on the braking force they can apply.

Now, since the kinetic energy of the car is 1/2*m*v^2, where m is the mass and v is the velocity, a car going twice as fast has four times the kinetic energy.

The amount of energy the brakes can dissipate equals the force they supply, multiplied by the distance traveled while braking. This means that over 10 feet, the brakes remove a certain amount of kinetic energy, regardless of the speed.

Since the car has four times the kinetic energy, it will take four times the distance to dissipate the energy and bring the car to a stop. So, the answer is c).

Answer 3

Four times

Answer 4

If you assume the brakes apply a constant amount of force, i.e. a constant amount of deceleration then the stopping distance will incease by a factor of 4

originally
v1(t) = -a*t + V_0
and the stopping time is t_f such that
0 = -a*t_f + V_0
then the stopping distance is x(t_f) = x_f
x(t) = -a/2*t^2 + V_0*t
x_f = -a/2*t_f^2 + V_0*t_f

if you double your initial velocity
v2(t) = -a*t + 2*V_0
then the stopping time doubles to 2*t_f
0 = -a*(2*t_f) + 2*V_0 = 2*(-a*t_f + V_0) = 0...
so then the new stopping distance is x(2*t_f)
-a/2*(2*t_f)^2 + 2*V_0*(2*t_f) = 4*(-a/2*t_f^2 + V_0*t_f) = 4*x_f

so the stopping distance has gone up by 4!

Answer 5

Wow, above is a long answer...

Using the 1/2mv^2 method as many other people have done will give you the answer of four.

He he, im a math genious :D Now back to fingerpainting...

Answer 6

No clue. You must be from MIT or Carnegie Melon or perhaps a DMV road test dude.. looks like it should be c. Post your answer when the question closes.

Answer 7

four times.

Answer 8

I think it's c.... this is math, not physics.