A car is moving at 36 miles per hour. The
kinetic energy of that car is 5 × 105 J.
How much energy does the same car have
when it moves at 115 miles per hour?
Answer in units of J
KE2 = KE1 * (V2/V1)^2
KE1 = 5*10^5 J.
V1 = 36 mi/h
V2 = 115 mi/h
Solve for KE2.
To find the amount of energy that the car has when it moves at 115 miles per hour, we can use the formula for kinetic energy, which is given by:
kinetic energy = 1/2 * mass * velocity^2
Since the mass of the car is not provided in the question, we can assume it to be constant for both cases.
Given:
Velocity of the car initially (v1) = 36 miles per hour
Kinetic energy initially (k1) = 5 × 10^5 J
Let's first convert the initial velocity from miles per hour to meters per second since the standard unit for kinetic energy is Joules (J):
1 mile = 1.60934 kilometers
1 hour = 3600 seconds
v1 = 36 miles/hour
= 36 * 1.60934 km/1 mile * 1000 m/1 km * 1 hour/3600 seconds
≈ 16.0934 m/s
Now we can substitute the given values into the formula for kinetic energy:
k1 = 1/2 * mass * v1^2
Solving for mass:
mass = 2 * k1 / v1^2
mass = 2 * 5 × 10^5 J / (16.0934 m/s)^2
mass ≈ 3.1103 kg (approximately)
Now, we can calculate the kinetic energy for the new velocity:
v2 = 115 miles/hour
= 115 * 1.60934 km/1 mile * 1000 m/1 km * 1 hour/3600 seconds
≈ 51.4998 m/s
Using the formula for kinetic energy:
k2 = 1/2 * mass * v2^2
= 1/2 * 3.1103 kg * (51.4998 m/s)^2
Calculating k2:
k2 ≈ 1/2 * 3.1103 kg * 2652.6196 m^2/s^2
k2 ≈ 4089 J
Therefore, the car has approximately 4089 Joules of energy when it moves at 115 miles per hour.