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how far will it take to stop under the same conditions if its initial velocity is 40 mph?‚Äč

Physics
Tutor: None Selected Time limit: 1 Day

If a car moving at 80 mph takes 400 ft to stop with uniform acceleration after its brakes are applied, how far will it take to stop under the same conditions if its initial velocity is 40 mph?

Oct 1st, 2014

Alright so first you have to take into account the equations of motions. You know that there are 4 of them;

v = u + at

v^2 - u^2 = 2as

s = ut + 1/2at^2

s = (u + v) / 2 x t

Among the above we choose the second equation. This is because all the physical quantities ( initial velocity, final velocity/ acceleration and distance) mentioned in the question is present in it. Therefore,

(80) ^2 - (0) ^2 = 2 x a x 122     [the distance is 122 due the conversion from foots to meters to make all  quantities                                                                                                                                                      have the same units]

By rearranging the equation, a = (80) ^2 / 2 x 122

                                                  = 6400 / 244

                                                  = 26 mph^2

Using this and the initial velocity as 40mph instead of 0mph in the same equation, we get the distance as:

s = (80)^2 - (40)^2 / 2 x 26

   = 6400 - 1600 / 52

   = 4800 / 52

   = 92 meters or 302 ft.


Oct 1st, 2014

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