a 1,000 kg car is rolling down the street at 2.5 m/s. How fast would a 2,500 kg car have to collide into it in order to bring it to rest(0 m/s) ?
To calculate the speed at which the 2,500 kg car would have to collide with the 1,000 kg car in order to bring it to rest, we need to apply the principle of conservation of momentum.
The principle states that the total momentum before a collision is equal to the total momentum after the collision. Mathematically, it can be written as:
Total initial momentum = Total final momentum
The momentum of an object is given by the product of its mass and velocity. Therefore, we can express the equation as:
(mass1 * velocity1) + (mass2 * velocity2) = 0
Where:
mass1 = mass of the 1,000 kg car
mass2 = mass of the 2,500 kg car
velocity1 = initial velocity of the 1,000 kg car (2.5 m/s)
velocity2 = final velocity of the 2,500 kg car (to be determined)
Substituting the given values into the equation, we get:
(1,000 kg * 2.5 m/s) + (2,500 kg * velocity2) = 0
Simplifying the equation, we have:
2,500 kg * velocity2 = -2,500 kg * 2.5 m/s
velocity2 = -2.5 m/s
Therefore, the 2,500 kg car would have to collide with the 1,000 kg car at a speed of -2.5 m/s (opposite direction) in order to bring it to rest (0 m/s).