Question

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.)

Answer 1

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

Step-by-step explanation:

`a=(V_f-V_0)/(t)`

isolating "t" from this equation:

`t=(V_f-V_0)/(a)`

Where:

a=
`-4.6m/s^2` (negative because is decelerating)

`V_f= 79 km/h`

`V_0= 114 km/h`

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

`79(km)/(h)*(1000m)/(1 km)*(1h)/(3600s)=(79*1000)/(3600)=21.94 m/s`

`114(km)/(h)*(1000m)/(1 km)*(1h)/(3600s)=(114*1000)/(3600)=31.67 m/s`

So;

`t=(V_f-V_0)/(a)=(21.94 m/s-31.66m/s)/(-4.6 m/s^2)=2.11 s`