Speed kills

You’re hired to advise the advertising agency making a Government information film on road safety. Their script for the film currently shows how much further a car travelling at 35 mph travels than one braking from 30 mph.

You don’t think this is punchy enough a message to get over and suggest that it would be more dramatic to show how fast the former is travelling at the point where the latter has come to a stop. They agree to hear your suggestion and the justification for it. What would you say to them?

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Hint

What assumptions can you make in order to tackle the problem with the familiar kinematic equations in S1.1 ?
 

Solution

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Solution

  • The key assumption here is that the braking acceleration of the car is (a) constant and (b) independent of the speed of travel.
  • We can then use the equation v2=u2+2as to analyse both situations.
  • In the first, the stopping distances are compared:
  • For car 1, travelling at 30 mph :

    $$s_1 = \frac{v_1^2 - u_1^2}{2a} = \frac{-900}{2a} \mbox{miles}$$

    (Note on units: I have not converted to ms-1. All speeds are in miles h-1, all accelerations in miles h-2)

  • Similarly for car 2, travelling at 35 mph :

    $$s_2 = \frac{v_2^2 - u_2^2}{2a} = \frac{-1225}{2a} \mbox{miles}$$

    Eliminating a,

    $$\frac{s_2}{s_1} = 1.36$$

  • In the second situation, the speed v2 is calculated after the second car has travelled the same distance that it takes the first car to come to a stop, s1.

    $$v_2^2 = u_2^2 + 2 a s_1 $$

    Using the expression for s1 calculated above :

    $$v_2^2 = 35^2 - 2a \times \frac{900}{2a} \Rightarrow v_2 = 18 \mbox{ mph}$$

  • Thinking about that, which would you find more dramatic?