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24 April, 16:22

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?

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  1. 24 April, 18:59
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    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 dа ta:

    (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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