the most common reasons for rear - end collisions are too short a following distance, speeding and failing brakes. car A of mass 1000 kg, stationary at a traffic light, is hit from behind by car B of mass 1200kg, travelling at 18m.s. immediately after the collision car A moves forward at 12m.s
Assume that linear momentum is conserved during this collision. calculate the speed of car B immediately after the collision.
You have to know the movement of both cars after the collision, not just car A.
To calculate the speed of car B immediately after the collision, we need to use the principle of conservation of linear momentum. Linear momentum is the product of an object's mass and velocity.
Step 1: Define the variables and equations:
- Mass of car A (m1) = 1000 kg
- Mass of car B (m2) = 1200 kg
- Initial velocity of car B (u2) = 18 m/s
- Final velocity of car A (v1) = 12 m/s
- Final velocity of car B (v2) = unknown (to be calculated)
By applying the principle of conservation of linear momentum, we can write the equation as follows:
(m1 * v1) + (m2 * u2) = (m1 * u1) + (m2 * v2)
Where u1 is the initial velocity of car A, which is 0 since it starts from rest.
Step 2: Substitute the known values into the equation:
(1000 kg * 12 m/s) + (1200 kg * 18 m/s) = (1000 kg * 0) + (1200 kg * v2)
Step 3: Solve for v2:
(12000 kg m/s) + (21600 kg m/s) = 1200 kg * v2
33600 kg m/s = 1200 kg * v2
Divide both sides by 1200 kg:
v2 = (33600 kg m/s) / 1200 kg
v2 = 28 m/s
Therefore, the speed of car B immediately after the collision is 28 m/s.