Question

Two small electric toy cars face each other at rest, separated by 5.00 m on the same track. Car 1 is switched on and accelerates at 1.00 m/s2 towards Car 2. Car 2 is switched on 1.0 s later, and accelerates at 2.00 m/s2 towards Car 1. When and where do the cars collide?

Answer 1

The time and distance required for car 1 to catch car 2 can be calculated using kinematic equations. By solving these equations with the given values, we find that the cars collide after 3.5 seconds and at a distance of 19.25 meters from the starting point of car 1.

Step-by-step explanation:

The time and distance required for car 1 to catch car 2 depends on the initial distance car 1 is from car 2 as well as the velocities of both cars and the acceleration of car 1. The kinematic equations describing the motion of both cars must be solved to find these unknowns. To solve the problem, we can calculate the time it takes for car 1 to reach car 2 by using the formula: time = (final velocity - initial velocity) / acceleration. Then we can substitute this time value into the formula for distance traveled: distance = initial velocity * time + 0.5 * acceleration * time^2. By plugging in the values given in the question, we can find that the cars collide after 3.5 seconds and at a distance of 19.25 meters from the starting point of car 1.