If a cars speed is tripled how much is the KE changed
The kinetic energy (KE) of an object is proportional to the square of its speed. If the speed of a car is tripled, we can calculate the change in kinetic energy as follows:
Let's assume the initial speed of the car is represented by "v". The initial kinetic energy (KE1) is given by KE1 = (1/2)mv^2, where "m" is the mass of the car.
When the car's speed is tripled, the new speed is represented by "3v". The new kinetic energy (KE2) is given by KE2 = (1/2)m(3v)^2 = (1/2)m(9v^2) = 4.5mv^2.
To determine the change in kinetic energy, we subtract the initial kinetic energy from the new kinetic energy:
Change in KE = KE2 - KE1 = 4.5mv^2 - (1/2)mv^2 = 4mv^2.
Therefore, if a car's speed is tripled, the kinetic energy changes by a factor of 4.
Explain why, if a cars speed is doubled or tripled, the K.E changes by a factor of 4
Apologies for the incorrect initial response. I misspoke and the correct answer is as follows:
If a car's speed is doubled, the kinetic energy (KE) changes by a factor of 4. If the speed is tripled, the KE changes by a factor of 9.
The kinetic energy of an object is given by the formula KE = (1/2)mv^2, where "m" represents the mass of the object and "v" represents its velocity.
If the speed is doubled, the new velocity becomes 2v. Substituting this value into the formula, we get KE2 = (1/2)m(2v)^2 = (1/2)mv^2 * 2^2 = (1/2)mv^2 * 4 = 4(1/2)mv^2 = 4KE1.
Similarly, if the speed is tripled, the new velocity becomes 3v. Substituting this value into the formula, we get KE2 = (1/2)m(3v)^2 = (1/2)mv^2 * 3^2 = (1/2)mv^2 * 9 = 9(1/2)mv^2 = 9KE1.
Therefore, if a car's speed is doubled, the kinetic energy changes by a factor of 4, and if the speed is tripled, the kinetic energy changes by a factor of 9.