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You are driving to the grocery store at 20 m/s. You are 110m from an intersection when the traffic light turns red. Assume that your reaction time is 0.50s and that your car brakes with constant acceleration. How far are you from the intersection when you begin to apply the brakes? What acceleration will bring you to rest right at the intersection? How long does it take you to stop after the light changes? the known values: vi=20m/s xi=110m t=.50s vf=0m/s xf=0m a=?
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As we know that reaction time will be

[tex]t = 0.50 s[/tex]

so the distance moved by car in reaction time

[tex]d = vt[/tex]

[tex]d = 20 \times 0.50[/tex]

[tex]d = 10 m[/tex]

now the distance remain after that from intersection point is given by

[tex]d = 110 - 10 = 100 m[/tex]

So our distance from the intersection will be 100 m when we apply brakes

now this distance should be covered till the car will stop

so here we will have

[tex]v_f = 0[/tex]

[tex]v_i = 20 m/s[/tex]

now from kinematics equation we will have

[tex]v_f^2 - v_i^2 = 2 a d[/tex]

[tex]0 - 20^2 = 2(a)100[/tex]

[tex]a = \frac{-400}{200} = -2 m/s^2[/tex]

so the acceleration required by brakes is -2 m/s/s

Now total time taken to stop the car after applying brakes will be given as

[tex]v_f - v_i = at[/tex]

[tex]0 - 20 = -2 (t)[/tex]

[tex]t = 10 s[/tex]

total time to stop the car is given as

[tex]T = 10 s + 0.5 s = 10.5 s[/tex]

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