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The question is:

A car can be stopped from initial velocity 84 km/h to rest in 55 meters. Assuming constant acceleration, find the stopping time.

Sorry for my ignorance, but I need to review physics knowledge. Can anyone explain me for this question?

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    $\begingroup$ It will always help if you can set out the progress you have made so far on answering the question $\endgroup$ – 410 gone Jan 1 '12 at 10:11
  • $\begingroup$ @EnergyNumbers: It would help if the problem was actually a well posed one. $\endgroup$ – Ron Maimon Jan 1 '12 at 17:50
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    $\begingroup$ As written this question seems to fail the concept-not-problem restriction in the FAQ for homework type question, but EnergyNumbers' answer is sufficiently conceptual that I'm minded to leave it open. $\endgroup$ – dmckee --- ex-moderator kitten Jan 2 '12 at 3:41
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    $\begingroup$ @dmckee: I think you are right. (One might argue that the question should be closed anyway, to indicate that it is inappropriate by our guidelines and to prevent more answers from being added unless/until it's improved... I'll leave it as your call.) $\endgroup$ – David Z Jan 2 '12 at 7:04
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Well, as the acceleration is constant you can use equations of uniform accelerated motion. Here, you are given with $v_0 = $ initial velocity, $d = $ distance traveled by car before stopping directly, and as the car eventually stops, hence you know the final velocity $v$, which is zero in this case.

Using two equations of motions, (a) $v^2 - v_0^2 = 2 a d$ and (b) $v = v_0 + at $ you can get the formula for time as,

$$ t = \frac{2d}{(v+v_0)}$$

Hence, calculate the time taken before stopping.

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Acceleration is the change in velocity per unit time. A constant acceleration is specified in the question: that means that the velocity will change by a constant amount, each second. Have a think about what that means, for the shape of the graph of velocity plotted against time. Can you express the area under that curve/line, as a function of its height (initial velocity) and its base length (stopping time)?

Velocity is distance travelled per unit time. So, what is represented by the area under the graph of velocity plotted against time?

Combining all of this, you should now have an expression for total distance travelled, expressed as a function of the initial velocity and the stopping time. And you can manipulate that equation so that stopping time is a function of total distance travelled and initial velocity.

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