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March 8th, 2009, 05:23 PM   #1
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car problem

2) A car is traveling at 100 km/hr when the brakes are applied. If the brakes can give
the car a constant negative acceleration of 8 m/s2,
a) how long will it take the car to come to a stop, and
b) how far will the car travel before stopping?
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March 8th, 2009, 06:40 PM   #2
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Re: car problem

No attempt at the problem...? This involves no calculus... this is just basic algebra and physics?

Start by converting units... 100km/hr * 1000m/1km * 1hr / 60min * 1min/60sec = 27.77m/s
Constant acceleration at 8m/s^2

It's easier to start with part b, in my opinion...

Part B:
v_F^2 = v_I^2 - 2 * a * d
0 = (27.77m/s)^2 - 2 * (-8m/s^2) * d
(16m/s^2)d = (27.77m/s)^2
d = (27.77m/s)^2/(16m/s^2) = 48.22530864m


Part A:
d = -1/2*a*t^2
(48.22530864m) * 2 = -a * t^2
sqrt [(48.22530864m * 2)] / -a = t
t = sqrt[(48.22530864m * 2)]/ -(-8m/s) = 3.472222222s
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March 11th, 2009, 06:12 PM   #3
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Re: car problem

Yes this problem can be done via Algebra but it can also be done using Calculus.

First you are given that the deceleration due to brake application is . If we define the function as acceleration with respect to time we then have:



Note however that the velocity of the car and the deceleration of the car use different units so first you must convert:



Continuing, by integrating the acceleration function we can get the function of the car's velocity, :



The initial velocity is when no time is passed, so and the initial velocity is given and can be used to solve for :




Therefore the function of velocity is then

From here the velocity must be zero for the car to be stopped so:




A)The car has stopped after applying the brakes for 3.47 seconds.

Similarly the rest of the problem follows that



In this case when no time has passed and because all of these functions are relative to the initial conditions and the car's initial position and the car has not traveled any distance from its initial position, 0:





Then at we know that the car has stopped and is its final position so:



B) The car will 48.23 meters before it comes to rest.

Note that the answers hold true to the same answers derived by Tyler using algebraic based physics formulas.
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