Question
A bicycle and rider have a total mass of 80 kilograms. This table lists the kinetic energy of the bicycle and rider at different speeds.
Kinetic Energy at Different Speeds
Speed
(km/h) Kinetic
Energy
(joules)
35 3780
20 1230
10 310
5 80
0 0
The line graph shows the relationship between the speed and kinetic energy of the bicycle and rider.
350_module_test_1.jpg
Describe the relationship between the speed and kinetic energy of the bicycle and rider. In your description, include whether the relationship is linear or nonlinear.
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Kinetic Energy at Different Speeds
Speed
(km/h) Kinetic
Energy
(joules)
35 3780
20 1230
10 310
5 80
0 0
The line graph shows the relationship between the speed and kinetic energy of the bicycle and rider.
350_module_test_1.jpg
Describe the relationship between the speed and kinetic energy of the bicycle and rider. In your description, include whether the relationship is linear or nonlinear.
Skip to input field
Answers
GPT-4o mini
The relationship between the speed and kinetic energy of the bicycle and rider is nonlinear. As the speed increases, the kinetic energy increases significantly at an accelerated rate. This is evident from the table of values, where the kinetic energy does not increase in a constant amount for each increment of speed.
For example, the increase in kinetic energy from 5 km/h to 10 km/h is relatively small (from 80 joules to 310 joules), while the increase from 20 km/h to 35 km/h shows a much larger change in kinetic energy (from 1230 joules to 3780 joules). This indicates that as speed increases, the kinetic energy increases at a faster rate.
Mathematically, the kinetic energy (KE) can be described by the formula:
\[ \text{KE} = \frac{1}{2} m v^2 \]
where \( m \) is the mass and \( v \) is the speed. Since kinetic energy depends on the square of the speed, this confirms the nonlinear relationship: as speed doubles, kinetic energy quadruples. Therefore, we can conclude that the relationship between speed and kinetic energy for the bicycle and rider is nonlinear, reflecting the squared dependence on speed.
For example, the increase in kinetic energy from 5 km/h to 10 km/h is relatively small (from 80 joules to 310 joules), while the increase from 20 km/h to 35 km/h shows a much larger change in kinetic energy (from 1230 joules to 3780 joules). This indicates that as speed increases, the kinetic energy increases at a faster rate.
Mathematically, the kinetic energy (KE) can be described by the formula:
\[ \text{KE} = \frac{1}{2} m v^2 \]
where \( m \) is the mass and \( v \) is the speed. Since kinetic energy depends on the square of the speed, this confirms the nonlinear relationship: as speed doubles, kinetic energy quadruples. Therefore, we can conclude that the relationship between speed and kinetic energy for the bicycle and rider is nonlinear, reflecting the squared dependence on speed.