A car is traveling at 14 m/s. How fast would the car need to go to double its kinetic energy? By what factor does the car's kinetic energy increase if its speed is doubled to 28 m/s?
We only get 3 chances and I'm on my last one before I get the question wrong, help?
not correct
To find the speed at which the car would need to go to double its kinetic energy, we can use the formula for kinetic energy:
Kinetic energy (KE) = 1/2 * mass * velocity^2
Let's assume the mass of the car remains constant.
To double the kinetic energy, we can set up the following equation:
2 * KE1 = KE2
Where KE1 is the initial kinetic energy and KE2 is the new kinetic energy.
Substituting the formula for kinetic energy, we get:
2 * (1/2 * m * v1^2) = 1/2 * m * v2^2
Canceling out the common terms, we have:
v1^2 = 2 * v2^2
Taking the square root of both sides, we get:
v1 = sqrt(2) * v2
So the car would need to travel at a speed equal to the square root of 2 times its current speed (14 m/s) to double its kinetic energy.
Now, to calculate the factor by which the car's kinetic energy increases when its speed is doubled to 28 m/s, we can use the formula for kinetic energy:
KE = 1/2 * mass * velocity^2
Let KE1 be the initial kinetic energy at speed v1 and KE2 be the new kinetic energy at speed v2.
The factor by which the kinetic energy increases can be calculated as:
Factor = KE2 / KE1
Substituting the formula for kinetic energy, we have:
Factor = (1/2 * m * v2^2) / (1/2 * m * v1^2)
Canceling out the common terms, we get:
Factor = (v2^2) / (v1^2)
Substituting the values, we have:
Factor = (28^2) / (14^2)
Calculating the value, we get:
Factor = 4
Therefore, if the car's speed is doubled to 28 m/s, its kinetic energy increases by a factor of 4.
Of course! I will guide you through the process step by step, so you can find the correct answers and avoid getting the question wrong.
To answer the first question, let's determine how fast the car would need to go to double its kinetic energy. Remember, kinetic energy (KE) is given by the equation KE = (1/2)mv^2, where m is the mass of the car and v is its velocity.
1. Begin by assuming the initial velocity of the car is 14 m/s and its mass remains constant.
2. Express the initial kinetic energy as KE1 = (1/2)m(14)^2.
3. Doubling the kinetic energy means the new kinetic energy (KE2) will be twice the initial value. So, KE2 = 2(KE1).
4. Substitute the expressions for KE1 and KE2 into the equation: (1/2)m(14)^2 * 2 = (1/2)m(v^2) and simplify.
5. Cancel out the mass and solve the equation to find the new velocity (v).
Now let's move on to the second question, which asks for the factor by which the car's kinetic energy increases if its speed is doubled to 28 m/s.
1. First, calculate the initial kinetic energy (KE1), assuming the car's speed is 14 m/s.
2. Then calculate the new kinetic energy (KE2) when the speed is doubled to 28 m/s.
3. The factor by which the kinetic energy increases can be found by dividing KE2 by KE1.
By following these steps, you can find the correct answers to both questions. Good luck on your last attempt!
KE is proportional to v^2
Or, v is proportional to sqrt KE
so if KE is doubled, v goes up by 1.414
if speed doubled, KE goes up by 4