Does the KE of a car change more when it
accelerates from 27 km/h to 37 km/h or when
it accelerates from 37 km/h to 47 km/h?
1. More information is needed.
2. No difference
3. From 37 km/h to 47 km/h
4. From 27 km/h to 37 km/h
Have you tried squaring the numbers? (Velocity is squared in the KE formula)
Compare (47)^2 - (37)^2 with
(37)^2 - (27)^2
Which is greater?
To determine which acceleration results in a greater change in kinetic energy (KE) of a car, we can use the equation for KE:
KE = 0.5 * m * v^2,
where m is the mass of the car and v is the velocity.
Comparing the two scenarios:
1. Accelerating from 27 km/h to 37 km/h:
- Initial velocity (v1) = 27 km/h
- Final velocity (v2) = 37 km/h
2. Accelerating from 37 km/h to 47 km/h:
- Initial velocity (v1) = 37 km/h
- Final velocity (v2) = 47 km/h
To determine which scenario has a greater change in kinetic energy, we need to compare the difference between the final and initial kinetic energies in both cases:
ΔKE1 = KE2 - KE1
ΔKE2 = KE3 - KE2
For option 1, we have:
ΔKE1 = 0.5 * m * v2^2 - 0.5 * m * v1^2
For option 2, we have:
ΔKE2 = 0.5 * m * v3^2 - 0.5 * m * v2^2
Since we don't know any information about the mass of the car, we cannot calculate the exact values of the change in kinetic energy in both cases. Therefore, the answer is: "More information is needed." (Option 1)
To determine which acceleration causes a greater change in kinetic energy (KE), we need to consider the equation for KE:
KE = (1/2) * m * v^2
Where:
KE = Kinetic Energy
m = mass of the car
v = velocity of the car
From the given options (1, 2, 3, and 4), the correct answer can be found by comparing the changes in kinetic energy for both scenarios mentioned.
1. More information is needed:
If the mass of the car (m) is not specified or known in both scenarios, it is impossible to determine which acceleration causes a greater change in kinetic energy. Therefore, more information is needed to answer the question.
2. No difference:
If the mass of the car (m) is the same in both scenarios, then the change in kinetic energy would be the same. Therefore, there would be no difference in the change of kinetic energy.
3. From 37 km/h to 47 km/h:
If the mass of the car (m) is the same, we can compare the changes in kinetic energy for both scenarios. As the car undergoes an increase in velocity from 37 km/h to 47 km/h, the change in kinetic energy will be greater compared to the change in kinetic energy when accelerating from 27 km/h to 37 km/h.
4. From 27 km/h to 37 km/h:
If the mass of the car (m) is the same, we can compare the changes in kinetic energy for both scenarios. As the car undergoes an increase in velocity from 27 km/h to 37 km/h, the change in kinetic energy will be less compared to the change in kinetic energy when accelerating from 37 km/h to 47 km/h.
Therefore, the correct answer is 3. From 37 km/h to 47 km/h.