Two cars are moving. The first car has twice the mass of the second car but only half as much kinetic energy. When both cars increase their speed by 3.41 m/s, they then have the same kinetic energy.
a) What is the original speed of the first car?
b)What is the original speed of the second car?
To solve this problem, we can use the formulas for kinetic energy and calculate the velocities of the two cars.
The formula for kinetic energy is:
Kinetic Energy = 1/2 * mass * velocity^2
We are given that the first car has twice the mass of the second car but only half as much kinetic energy. Let's assign variables to the masses and velocities of the two cars:
Let m1 and v1 represent the mass and velocity of the first car respectively.
Let m2 and v2 represent the mass and velocity of the second car respectively.
According to the given information, we have the following equations:
1) m1 = 2m2 (The first car has twice the mass of the second car)
2) 1/2 * m1 * v1^2 = 2 * (1/2 * m2 * v2^2) (The first car has only half as much kinetic energy as the second car)
3) v1 + 3.41 = v2 + 3.41 (Both cars increase their speed by 3.41 m/s)
Let's solve these equations to find the original velocities of the two cars:
a) To find the original speed of the first car (v1):
We substitute m1 = 2m2 from equation 1 into equation 2:
1/2 * (2m2) * v1^2 = 2 * (1/2 * m2 * v2^2)
Simplifying the equation:
m2 * v1^2 = m2 * v2^2
Since the masses cancel out, we have:
v1^2 = v2^2
Taking the square root of both sides, we get:
v1 = v2
From equation 3, we know v1 + 3.41 = v2 + 3.41. Therefore, v1 = v2.
So the original speed of the first car (v1) is equal to the original speed of the second car (v2).
b) To find the original speed of the second car (v2):
From equation 3, we have:
v1 + 3.41 = v2 + 3.41
Substituting in v1 = v2, we can simplify the equation to:
v2 + 3.41 = v2 + 3.41
This equation tells us that the original speed of the second car is the same as its final speed.
Therefore, the original speed of the second car is 0 m/s.
To summarize:
a) The original speed of the first car (v1) is equal to the original speed of the second car (v2).
b) The original speed of the second car (v2) is 0 m/s.