The brakes on your automobile are capable of creating a deceleration of 4.9 m/s2. if you are going 149 km/h and suddenly see a state trooper, what is the minimum time in which you can get your car under the 100 km/h speed limit?

You need at least 2.8 s to slow down your car to 100 km/h. If we add reaction time (≅0.3 s), you will need 3.1 s.

Explanation:

Hi there!

The equation of velocity for an object moving in a straight line is the following:

v = v0 + a · t

Where:

v = velocity at time t.

v0 = initial velocity.

a = acceleration.

t = time.

We have to find the time at which the velocity is 100 km/h with a decceleration of 4.9 m/s² and an initial velocity of 149 km/h. Let´s first convert km/h into m/s:

149 km/h · (1000 m / 1 km) · ( 1 h / 3600 s) = 41.4 m/s

100 km/h · (1000 m / 1 km) · ( 1 h / 3600 s) = 27.8 m/s

Now, let´s solve the equation of velocity for the time:

v = v0 + a · t

(v - v0) / a = t

Replacing with the data:

(27.8 m/s - 41.4 m/s) / -4.9 m/s² = t

Notice that the acceleration is negative because you are slowing down.

t = 2.8 s

You need at least 2.8 s to slow down your car to 100 km/h. If we add reaction time (≅0.3 s), you will need 3.1 s.

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