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Old Sep 27th 2008, 03:14 PM   #1
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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!
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Old Sep 27th 2008, 03:31 PM   #2
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Originally Posted by meredith xo cheer View Post
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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Old Sep 27th 2008, 05:46 PM   #3
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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
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