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Calculating acceleration when only have time and distance

  1. Nov 30, 2015 #1
    1. The problem statement, all variables and given/known data
    A car travels 400m in 60s. The first 10s it accelerates from stationary. The last 10 seconds it decelerates back to stationary. For the middle 40s it has a constant velocity. What is the acceleration?

    2. Relevant equations
    None given

    3. The attempt at a solution
    Using only time and distance travelled I can only think how to calculate the average velocity: Vave = distance travelled / time = 6.67 m/s. I don't so much need an answer, more some guidance of where to begin. I'm pretty stuck. Thanks
     
  2. jcsd
  3. Nov 30, 2015 #2

    gneill

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    Staff: Mentor

    Maybe start graphically? You might find some inspiration. Make a sketch of velocity versus time. You don't know the cruising speed yet, so leave that as a variable. Now, what do you know about the area under a velocity vs time graph?
     
  4. Nov 30, 2015 #3
    The area under the graph should equal the displacement, so the total area should equal 400m. I have drawn a graph (attached). When a put the acceleration and deceleration together the area is exactly one 5th of the time spent cruising: therefore, the amount of time spent accelerating and decelerating is one 5th of 400m = 80 meters. Divide this by 2 and the car moved 40 meters in 10 seconds.
    Acceleration = distance/time^2 = 40m/10^2 = 0.4m/s

    Does this sound right? Making a sketch was good advise because it is starting to make sense to me. Just hope I have taken a wrong turn somewhere.
    Thanks :)
     

    Attached Files:

  5. Nov 30, 2015 #4

    gneill

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    Staff: Mentor

    Very close indeed. However: ##distance = \frac{1}{2} Acceleration \cdot time^2##. So fix that up and you should be good.
     
  6. Nov 30, 2015 #5
    Yay! Thank you for your help. I've been staring at this question since yesterday, and actually drawing it was brilliant advice. Thank you!
     
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