Answer :
Final answer:
The kinetic energy of the scooter when its speed doubles to 14 m/s is 1568 J, calculated using the formula KE = ½ mv².
Explanation:
To calculate the kinetic energy (KE) of the moving scooter when its speed doubles, we can use the equation for kinetic energy:
KE = ½ mv².
In the initial condition, the kinetic energy can be calculated as follows:
KE = ½ (16 kg) (7 m/s)² = ½ (16) (49) = 56 × 8 = 448 J.
When the speed of the scooter doubles, it goes from 7 m/s to 14 m/s. Calculating the new kinetic energy:
KE = ½ (16 kg) (14 m/s)² = ½ (16) (196) = 1568 J.
Therefore, the correct answer is 1568 J, which means choice b is the correct one.
The formula for kinetic energy is:
KE = 0.5mv^2
where:
m = mass
v = speed
Given this formula, the original KE of the scooter is calculated as 392 J. Since the speed is doubled, it can be observed in the formula that the change would actually affect the kinetic energy by quadrupling it. This is because 2^2 is 4. So, 392(4) = 1568 J or B.
KE = 0.5mv^2
where:
m = mass
v = speed
Given this formula, the original KE of the scooter is calculated as 392 J. Since the speed is doubled, it can be observed in the formula that the change would actually affect the kinetic energy by quadrupling it. This is because 2^2 is 4. So, 392(4) = 1568 J or B.
