Car X passes car Y on a motorway. Car X is travelling at 1.5 times the speed of car Y. The mass of car X is 5/4 of the mass car Y. How do the kinetic energies of the two cars compare?
(the answer is KE (X) = 1.80 * KE (Y))
KEx=1/2 m v^2=1/2 1.25 (1.5)^2
KEy=1/2 m v^2
kex/key=1.5^2 * 1.25 Not your answer.
Are you certain it did not read "The mass of car Y is 5/4 of the mass car X" That would give you the answer you proposed ...4/5 * 1.5^2
To compare the kinetic energies of the two cars, we need to use the equation for kinetic energy:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
Let's analyze each car separately to find their respective kinetic energies.
For car Y:
Given that car X is traveling at 1.5 times the speed of car Y, the velocity of car Y can be represented as v.
Kinetic Energy (KEY) = (1/2) * massY * v^2
For car X:
Since car X is traveling at 1.5 times the speed of car Y, its velocity can be expressed as 1.5v.
Kinetic Energy (KEX) = (1/2) * massX * (1.5v)^2
Given that the mass of car X is 5/4 of the mass of car Y, we can write:
massX = (5/4) * massY
Substituting this expression into the equation for KEX:
KEX = (1/2) * ((5/4) * massY) * (1.5v)^2
= (5/8) * massY * (2.25v^2)
= (5/8) * (2.25) * massY * v^2
= (1.40625) * massY * v^2
Therefore, we can conclude that the kinetic energy of car X (KEX) is equal to 1.40625 times the kinetic energy of car Y (KEY):
KEX = 1.40625 * KEY
However, this does not match the given answer of 1.80. It's possible that there was an error in the calculation or in the provided answer.