A car is moving at 53 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 102 miles per hour?
Answer in units of J
HELP!!!!
I've tried doing (5*10 J)* (102/53)^2 and I keep on getting it wrong PLEASE HELP ME UNDERSTAND
1) KE=1/2*m*v^2
(KE*2)/v^2=m
2) KE=m*v^2
use the mass we found and convert mph to m/s
2) KE=1/2*m*v^2
sorry about that.
To calculate the energy of the car when it moves at a different velocity, we can use the equation for kinetic energy:
KE = 1/2 * m * v^2
Where KE is the kinetic energy, m is the mass of the car, and v is the velocity of the car.
In this case, we are given the kinetic energy as 5 × 10^5 J when the car is moving at 53 mph. We need to find the energy when it moves at 102 mph.
To solve this problem, we need to make sure we are using consistent units.
First, let's convert the velocity from mph to m/s:
53 mph * (0.44704 m/s) / (1 mph) = 23.77232 m/s (rounded to 5 decimal places)
Now, let's square the velocity:
(23.77232 m/s)^2 = 565.450862 m^2/s^2 (rounded to 6 decimal places)
Next, we need to find the energy when the car moves at 102 mph.
102 mph * (0.44704 m/s) / (1 mph) = 45.72048 m/s (rounded to 5 decimal places)
Now, let's calculate the kinetic energy using the equation:
KE = 1/2 * m * v^2
Substituting the values:
KE = 1/2 * m * (45.72048 m/s)^2
Now, we need to solve for m, the mass of the car. To do that, we can rearrange the equation:
m = KE / (1/2 * v^2)
Now, let's plug in the given kinetic energy and velocity:
m = (5 × 10^5 J) / (1/2 * (45.72048 m/s)^2)
m = (5 × 10^5 J) / (1/2 * 2089.437597 m^2/s^2)
m = (5 × 10^5 J) / 1044.718798 m^2/s^2
m ≈ 478.713548 kg (rounded to 6 decimal places)
Finally, we have found the mass of the car when it moves at 102 mph. Now, we can find the kinetic energy at this velocity:
KE = 1/2 * (478.713548 kg) * (45.72048 m/s)^2
KE ≈ 1.031 × 10^6 J (rounded to 3 decimal places)
Therefore, when the car moves at 102 mph, it has approximately 1.031 × 10^6 joules of energy.
The kinetic energy is 5 x 10^5
So make sure to type (5*10^5J)*(102/53)^2