Question
A student rides her bicycle down a hill. Together, she and the bicycle have a mass of 56 kilograms. She is moving at 11 meters per second. What is her kinetic energy?(1 point)
Responses
17,248 J
6,776 J
13,552 J
3,388 J
Responses
17,248 J
6,776 J
13,552 J
3,388 J
Answers
GPT-4o mini
The kinetic energy (KE) of an object can be calculated using the formula:
\[
KE = \frac{1}{2} m v^2
\]
where:
- \( m \) is the mass of the object (in kilograms),
- \( v \) is the velocity of the object (in meters per second).
Given:
- \( m = 56 \) kg,
- \( v = 11 \) m/s,
we can substitute the values into the formula:
\[
KE = \frac{1}{2} \times 56 \, \text{kg} \times (11 \, \text{m/s})^2
\]
Calculating \( (11 \, \text{m/s})^2 \):
\[
(11 \, \text{m/s})^2 = 121 \, \text{m}^2/\text{s}^2
\]
Now, substituting back:
\[
KE = \frac{1}{2} \times 56 \times 121
\]
Calculating \( 56 \times 121 \):
\[
56 \times 121 = 6776
\]
Now divide by 2:
\[
KE = \frac{6776}{2} = 3388 \, \text{J}
\]
Therefore, the kinetic energy is:
\[
\boxed{3,388 \, \text{J}}
\]
\[
KE = \frac{1}{2} m v^2
\]
where:
- \( m \) is the mass of the object (in kilograms),
- \( v \) is the velocity of the object (in meters per second).
Given:
- \( m = 56 \) kg,
- \( v = 11 \) m/s,
we can substitute the values into the formula:
\[
KE = \frac{1}{2} \times 56 \, \text{kg} \times (11 \, \text{m/s})^2
\]
Calculating \( (11 \, \text{m/s})^2 \):
\[
(11 \, \text{m/s})^2 = 121 \, \text{m}^2/\text{s}^2
\]
Now, substituting back:
\[
KE = \frac{1}{2} \times 56 \times 121
\]
Calculating \( 56 \times 121 \):
\[
56 \times 121 = 6776
\]
Now divide by 2:
\[
KE = \frac{6776}{2} = 3388 \, \text{J}
\]
Therefore, the kinetic energy is:
\[
\boxed{3,388 \, \text{J}}
\]