Car Speed for 1kW Home Power Usage

[Physics211]

Homework Statement

The power consumption by a typical house is 1 kW. If the kinetic energy of a car (mass 130 kg) is equal to the total energy used by the house in 1.2 minute, what is the car’s speed?

Homework Equations

P=W/t
P=Fv
P:Power

The Attempt at a Solution

I converted 1kW to 1000 Watts and 1.2 minutes to 72 seconds and put it into the first equation but don't know how to get F for the second equation.

 

[lewando]

Consider:

Energy = Power * time

and

Kinetic Energy = mv²/2

 

[zgozvrm]

Do you mean to say that the power consumed by a typical house is 1 kWh?

 

[lewando]

It is better to say that the house consumes energy at the rate of 1kW. Exactly like the wattage rating on a light bulb. If the house is "on" for 1.2 minutes then you can determine the energy consumed by the house during this interval by:

Energy = Power * time

 

[rwisz]

To solve this problem, we need to use the concept of work and energy. The work done by the car is equal to the kinetic energy it possesses. So, we can equate the work done by the car to the total energy used by the house.

W = Ek (kinetic energy)

We can calculate the kinetic energy of the car using the formula:

Ek = 1/2 mv^2

Where:
m = mass of the car = 130 kg
v = speed of the car

Substituting the given values, we get:

W = 1/2 (130 kg) v^2

Now, we can equate the work done by the car to the power consumed by the house:

W = P x t

Where:
P = power consumed by the house = 1000 Watts
t = time taken = 72 seconds

Substituting the given values, we get:

1/2 (130 kg) v^2 = 1000 Watts x 72 seconds

Solving for v, we get:

v = √(2 x 1000 Watts x 72 seconds / 130 kg)

v = √(144000 / 130) m/s

v = √1107.69 m/s

Therefore, the speed of the car is approximately 33.26 m/s.