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I have the question

"A car brakes from a speed of $110\dfrac{km}{h}$ to rest in a time of $8.0s$ with a uniform acceleration. Calculate its acceleration while braking and the distance it travels.

Use $g=9.81\dfrac{m}{s}$ as the acceleration due to gravity. Assume air resistance is negligible".

I know that $F = ma$ (Force = mass $\times$ acceleration),

Therefore, acceleration $a = \dfrac{F}{m}$.

However there is no force or mass given in the question and so I am not sure on how to find the cars acceleration while braking and the distance it travels.

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    $\begingroup$ Do you know the big 5 physics equations? Try a google search. $\endgroup$ – Kaynex Jan 19 '17 at 15:36
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    $\begingroup$ Sometimes a problem statement includes irrelevant data, so that you develop the skill of picking the important data when addressing a real-world problem. Which data are irrelevant to this question? You already seem to have a hunch. $\endgroup$ – Fabio Somenzi Jan 19 '17 at 15:43
  • $\begingroup$ @MyGlasses units should be in roman type $\endgroup$ – Fabio Somenzi Jan 19 '17 at 16:04
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First of all, converting $\text{kmh}^{-1}$ into $\text{ms}^{-1}$ would be helpful.

You do not need to use the mass at all. Using Newton's laws of constant acceleration works fine.

For finding the acceleration, use $v=u+at$, where $v$ is the final velocity, $u$ is the initial velocity and $t$ is the time and $a$ is the mean acceleration of the car.

For finding the distance travelled, use $s=ut+\frac{1}{2}at^2$ or $v^2=u^2+2as$ (You can use both). $s$ is the displacement of the car from when the car starts to brake.

Feel free to comment the answers you get from doing this.

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  • $\begingroup$ Thank you (: however I do not understand the displacement s. $\endgroup$ – Dan Khan Jan 19 '17 at 16:02
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    $\begingroup$ @Dan Distance is a scalar quantity which determines how much an object has covered during its motion. Displacement is a vector quantity which determines how far it is out of position. In your case, the displacement does equal to the distance. $\endgroup$ – projectilemotion Jan 19 '17 at 16:06
  • $\begingroup$ For the distance using the formula s = ut + 1/2 at$^2$ I get the answer 0.37 for the distance however the solutions say that the distance should be 0.12 km. what have I done wrong ? I have set u = 30.6, a = 3.8, and t = 8.0. $\endgroup$ – Dan Khan Jan 19 '17 at 16:11
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    $\begingroup$ @Dan Note that your acceleration should be $a=-3.8$, since the car is decelerating. $\endgroup$ – projectilemotion Jan 19 '17 at 16:15
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For uniform acceleration you have $v=v_0+at, s=s_0+v_0t+\frac 12at^2$ with $v$ velocity, $s$ distance, and the sub zeros are the starting conditions. $g$ has nothing to do with this. Use the data you have to solve for $a,t, s$

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