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The brakes on your automobile are capable of creating a deceleration of 4.6 m/s^2. If you are going 114 km/h and suddenly see a state trooper, what is the minimum time in which you can get your car under the 79 km/h speed limit? (The answer reveals the futility of braking to keep your high speed from being detected with a radar or laser gun.)

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Answer:

The minimum time to get the car under max. speed limit of 79 km/h is 2.11 seconds.

Explanation:

[tex]a=\frac{V_f-V_0}{t}[/tex]

isolating "t" from this equation:

[tex]t=\frac{V_f-V_0}{a}[/tex]

Where:

a=[tex]-4.6m/s^2[/tex] (negative because is decelerating)

[tex]V_f= 79 km/h[/tex]

[tex]V_0= 114 km/h[/tex]

First we must convert velocity from km/h to m/s to be consistent with units.

[tex]79\frac{km}{h}*\frac{1000m}{1 km}*\frac{1h}{3600s}=\frac{79*1000}{3600}=21.94 m/s[/tex]

[tex]114\frac{km}{h}*\frac{1000m}{1 km}*\frac{1h}{3600s}=\frac{114*1000}{3600}=31.67 m/s[/tex]

So;

[tex]t=\frac{V_f-V_0}{a}=\frac{21.94 m/s-31.66m/s}{-4.6 m/s^2}=2.11 s[/tex]

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