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 Kinematics and Dynamics Kinematics and Dynamics Physics Help Forum Sep 27th 2008, 03:14 PM #1 Junior Member   Join Date: Sep 2008 Posts: 6 word problem - velocity, acceleration, time two cars are traveling along a straight road, one behind the other. the first is traveling at a constant velocity of 12 m/s. the second, approaching from the rear, is traveling at 25 m/s. when the second car is 200m behind the first, the driver applies the brakes, producing a constant acceleration of -0.20 m/s^2. will the cars crash and if so, where and when? thansk so much to anyone that can help i really appreciate it!   Sep 27th 2008, 03:31 PM   #2
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 Originally Posted by meredith xo cheer two cars are traveling along a straight road, one behind the other. the first is traveling at a constant velocity of 12 m/s. the second, approaching from the rear, is traveling at 25 m/s. when the second car is 200m behind the first, the driver applies the brakes, producing a constant acceleration of -0.20 m/s^2. will the cars crash and if so, where and when? thansk so much to anyone that can help i really appreciate it!
Let the origin be where the second car is at when the first applies the brakes. I am taking a positive direction as the direction of the initial velocity of either car.

We know that the second car's equation of motion is
$\displaystyle x = x_0 + vt$

$\displaystyle x = vt$
since the car starts at the origin.

For the first car we have
$\displaystyle x = x_0 + v_0t + \frac{1}{2}at^s$
where $\displaystyle x_0 = 200$, $\displaystyle v_0 = 12$, and $\displaystyle a = -0.2$ (in the appropriate units.)

The cars will meet at the same x values and the same t value. So we need to solve the system:
$\displaystyle x = 25t$
and
$\displaystyle x = 200 + 12t - 0.1t^2$

Subbing the first equation into the second:
$\displaystyle 25t = 200 + 12t - 0.1t^2$

$\displaystyle 0.1t^2 + 13r - 200 = 0$

Solve for t and sub it into either of the original equations to get x.

-Dan
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See the forum rules here.   Sep 27th 2008, 05:46 PM #3 Junior Member   Join Date: Sep 2008 Posts: 6 thanks so much your work makes perfect sense but i think you put the acceleration with the wrong car? so in that case im still not sure what to do any ideas? Last edited by meredith xo cheer; Sep 27th 2008 at 05:47 PM. Reason: forgot something  Tags acceleration, physics, problem, time, velocity, word Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post TKJ Kinematics and Dynamics 1 Oct 17th 2015 05:30 PM Devlan Advanced Mechanics 2 Mar 13th 2014 12:07 AM dcebb2001 Kinematics and Dynamics 22 Feb 1st 2013 11:22 PM bradycat Thermodynamics and Fluid Mechanics 0 Nov 9th 2011 06:05 PM ariol Kinematics and Dynamics 1 Jan 8th 2009 10:08 PM 