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Constant Acceleration problem

  1. Aug 28, 2011 #1
    1. A car sits on a freeway entrance ramp waiting for a break in traffic. The driver sees a gap and accelerates onto the freeway. Thar car starts from rest and moves in a straight line and has a speed of 20m/s when it reaches the end of the 120 m long ramp. Find A] acceleration of the car. B] How much time does it take the car to drive the entire length of the ramp?



    2. EQNs of constant acceleration
    Vx=Vox+AxT
    X=Xo+VoxT+1/2AxT
    Vx2=Vox2+2Ax(X-Xo)
    X-Xo=((Vox+Vx)/2)T




    3. I cannot find the acceleration if I do not know the time it took to get to the end point. I am also stuck on the idea that if you have constant velocity you must have constant acceleration. But, arent external forces always slowing you down, so to maintain constant velocity you would always need to be accelerating?
     
  2. jcsd
  3. Aug 28, 2011 #2

    lewando

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    Gold Member

    You know V0x, Vx, x0, and x. Assume constant acceleration, a.

    Why cant you use your 3rd equation to find a?

    For constant velocity you need constant acceleration, provided that the constant acceleration is the constant zero.

    Depending on the direction of the "external forces" they could be speeding you up, as well. Short answer: no.
     
  4. Aug 28, 2011 #3

    PeterO

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    Homework Helper

    As mentioned in the previous post, zero is a constant !


    This sounds like you are using the description "external forces" for friction.

    Some external forces could be trying to slow you down, some could be trying to speed you up. Some may be trying to make you veer left, others may be trying to make you veer right.

    If the sum of all the external forces is zero, you will have constant velocity.

    Imagine that car on the freeway ramp. You know that if the driver "floors" the accelerator, the car will quickly gain speed along the ramp.
    Suppose the driver decided to hold the accelerator to the floor. Will the car eventually reach a speed where it could crest a rise and go into orbit with the International Space Station? [you can look up / claculate the speed of the space station in orbit to see how fast the car might have to go].
    neither of us believe that - we know that once the car reaches a certain speed [perhaps 120 mph or 200 km/h, it just can't go any faster.

    Another alternate explanation might be that the car manufacturer has secretly included a magical resistance measuring device, which is calibrated so that as soon as the air resistance reaches a certain level, the engine cuts out so the car cannot go any faster. That would certainly explain why you can drive just that little bit faster with a tail wind than with a head wind.
    Neither of us believe that either [I hope]

    In reality, the engine of the car produces a lot of power. Some of that is "lost" thrashing the oil and gears around in the gearbox etc. The rest is transmitted, via the tyres, to the road [it means the road surface and the tyres have to be up to the task. Grass is no good, the wheels just spin and you go nowhere]. Newtons 3rd law, the tyres push back on the road - the road pushes forward on the car. That force of the road on the car tends to accelerate it.
    That driving force remains pretty well constant [the size of the force does vary with speed, but only because as the car goes faster, the engine spins faster and most engines produce slightly different driving forces at different engine speeds.
    The main force that changes is the air resistance. If you have ever put your hand out the window into the airstream an high speed you will be aware of that.
    Eventually the Force of air resistance trying to slow you, and the driving force originating from the engine balance each other so you continue at constant velocity.
     
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