Question

Two cars (1) and (2) move on the same straight road moving at opposite speeds so that they approach each other, and at time t=0 they are at a distance of d = 180 m. The car (2) performs linear constant velocity motion, while the car (1) uniformly accelerating motion with acceleration of measure a = 2 m / s². The two cars collide at time t=10 s. What is the measure of the speed of the two cars at time t=0?

a) The speed of car (2) is 20 m/s, and the speed of car (1) is 0 m/s.
b) The speed of car (2) is 0 m/s, and the speed of car (1) is 20 m/s.
c) The speed of car (2) is 10 m/s, and the speed of car (1) is 10 m/s.
d) The speed of car (2) is 2 m/s, and the speed of car (1) is 18 m/s.

Answer 1

The speed of car (1) is 20 m/s and the speed of car (2) is 0 m/s at time t=0.

Step-by-step explanation:

Two cars (1) and (2) are moving towards each other on a straight road. Car (1) is uniformly accelerating with an acceleration of 2 m/s², while car (2) is moving with a constant velocity. The cars collide at time t=10 s, and at that time, the distance between them is 180 m.

To determine the speed of the cars at time t=0, we need to find their initial velocities. Since car (1) is undergoing uniformly accelerating motion, we can use the equation:

v = u + at

Where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the final velocity is 0 m/s because the cars collide and come to a stop.

Substituting the values into the equation, we get:

0 = u + 2(10) → u = -20 m/s

Therefore, the speed of car (1) at time t=0 is 20 m/s, and the speed of car (2) at time t=0 is 0 m/s. Answer choice (b) is correct.