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Question from Android, a student:

At a certain instant, two cars A and B are 2000 ft apart. At this instant, car A is traveling at 15 miles/hr. and accelerating at 3 ft/s^2 while B is moving towards A at 30 miles/hr. and an acceleration of 2 ft/s^2.

Find the ff:
a.) The possible time of their collusion in minutes.
b.) The distance in ft. each has traveled before collusion.

Hi Android,

The displacement $d$ of a body moving along a line with uniform acceleration is $d = v_0 t + \frac12 a c^2$ where $v_0$ is the initial velocity, $t$ is the time and $a$ is the acceleration. Suppose you start your clock at the instant the cars are 2000 feet apart.

First express the velocities of the cars in feet per second. After $t$ seconds how far has the first car travelled? How far has the second car travelled? What is the sum of the distances the two cars have travelled in $t$ seconds? At what time $t$ is this sum equal to 2000 feet?

I hope this helps,


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