Select the correct answer.
Julie is cycling at a speed of 3.4 meters/second. If the combined mass of the bicycle and Julie is 30 kilograms, what is the kinetic energy?
A. $1.7 \times 10^2$ joules
B. $1.5 \times 10^2$ joules
C. $2.0 \times 10^2$ joules
D. $2.2 \times 10^2$ joules
Answer (1)
Use the kinetic energy formula: K E = 2 1 m v 2 .
Substitute the given values: m = 30 kg and v = 3.4 m/s.
Calculate the kinetic energy: K E = 2 1 × 30 × ( 3.4 ) 2 = 173.4 joules.
Select the closest answer from the options: 1.7 × 1 0 2 joules.
Explanation
Problem Analysis We are given that Julie is cycling at a speed of 3.4 meters/second, and the combined mass of the bicycle and Julie is 30 kilograms. We need to find the kinetic energy.
Kinetic Energy Formula The formula for kinetic energy (KE) is given by: K E = 2 1 m v 2 where m is the mass in kilograms (kg) and v is the velocity in meters/second (m/s).
Substitution We are given m = 30 kg and v = 3.4 m/s. Substituting these values into the formula, we get: K E = 2 1 × 30 × ( 3.4 ) 2
Calculation Now, we calculate the kinetic energy: K E = 2 1 × 30 × ( 3.4 ) 2 = 15 × ( 3.4 ) 2 = 15 × 11.56 = 173.4 The kinetic energy is 173.4 joules.
Comparison and Selection Comparing our calculated value (173.4 joules) with the given options: A. 1.7 × 1 0 2 joules = 170 joules B. 1.5 × 1 0 2 joules = 150 joules C. 2.0 × 1 0 2 joules = 200 joules D. 2.2 × 1 0 2 joules = 220 joules
The closest value to our calculated kinetic energy (173.4 joules) is option A, 1.7 × 1 0 2 joules, which is 170 joules.
Final Answer Therefore, the correct answer is A. 1.7 × 1 0 2 joules.
Examples
Kinetic energy is a fundamental concept in physics that describes the energy of motion. For example, when designing vehicles, engineers must consider the kinetic energy involved in collisions to ensure safety. Similarly, in sports, understanding kinetic energy helps athletes optimize their movements for better performance, such as maximizing the kinetic energy of a baseball when hitting it or a soccer ball when kicking it. The formula K E = 2 1 m v 2 is crucial in these applications.
