Question

Two cars drive on a straight highway. At time t=0, car 1 passes road marker 0 traveling due east with a speed of 20.0 m/s . At the same time, car 2 is 1.00km east of mile marker 0 traveling at 30.0m/s due west. Car 1 is speeding up with an acceleration of magnitude 2.5m/s^2 , and car 2 is slowing down with an acceleration of magnitude -3.2 m/s^2 .

A) Write position time equation for both cars let east be the positive direction
B) At what time do the cars pass next to one another?

Answer 1

The position-time equations for two cars with given acceleration can be used to determine when they will pass each other by equating their positions and solving the resulting quadratic equation for time.

Step-by-step explanation:

To solve the problem of finding when two cars driving on a straight highway pass each other, we first need to establish equations for the position of each car as a function of time (t), taking into account the given acceleration and initial velocities.

For car 1 which starts from road marker 0 and travels due east, its initial velocity (v1i) is 20.0 m/s, and it accelerates at 2.5 m/s2. Its position-time equation, with east as the positive direction, is:

• x1(t) = x1i + v1it + 0.5a1t2 = 0 + (20.0 m/s)t + 0.5(2.5 m/s2)t2

For car 2 which starts 1.00 km east (1000 m) and travels west, its initial velocity (v2i) is -30.0 m/s (negative because it is westward), and it decelerates at 3.2 m/s2(also negative). Its position-time equation is:

• x2(t) = x2i + v2it + 0.5a2t2 = 1000 m + (-30.0 m/s)t + 0.5(-3.2 m/s2)t2

To find when the cars pass next to one another, we set x1(t) = x2(t) and solve for t. This is a quadratic equation which can be solved either by factoring, completing the square, or using the quadratic formula.