Constant Velocity - Collision Course

Summary

The video demonstrates how to find where two toy cars moving at constant velocity will collide. The red car starts at −3.2 m and moves right at +0.80 m/s. The blue car starts at +7.0 m and moves left at −2.40 m/s. Right is defined as positive, making the direction of each velocity explicit.

For constant-velocity motion, the presenter uses:

[ x_f = vt + x_i ]

Because the cars collide, they must be at the same position at the same time. Applying the motion equation to each car gives:

• Red: (x_f = 0.80t - 3.2)
• Blue: (x_f = -2.40t + 7.0)

Setting these positions equal and solving gives a collision time of approximately 3.19 seconds. Substituting that time into either equation gives a collision position of approximately −0.65 m. Thus, the cars meet 0.65 m to the left of the origin.

Method

1. Choose a coordinate direction. In this example, right is positive and left is negative.
2. Sketch the situation. Mark the origin, both starting positions, and each car’s direction of motion.
3. Record the knowns and unknowns for each car. Keep separate data for the time, velocity, initial position, and final position of each car.
4. Include signs and units. The red car’s velocity is (+0.80\ \text{m/s}), and the blue car’s is (-2.40\ \text{m/s}). Their initial positions are −3.2 m and +7.0 m.
5. Write a constant-velocity equation for each car: (x_f = vt + x_i).
6. Apply the collision conditions. At impact, both cars have the same final position and have traveled for the same amount of time.

7. Set the position equations equal and solve for time: [ 0.80t - 3.2 = -2.40t + 7.0 ] This gives (t = 3.1875\ \text{s}).

8. Substitute the time into either motion equation to find the meeting position: (x_f \approx -0.65\ \text{m}).

9. Check whether the result makes sense. The negative position places the collision left of the origin, consistent with the diagram.

The main lesson is to track signs carefully and use the shared time and position at the collision to connect the two motion equations.

Speaker or Source

• Mr. Werman — the video’s instructor and narrator.