Question

F(x)=0.145x^2

The function above models f, the kinetic energy, in joules, of a baseball traveling at a speed of x meters per second. Based on the function, what is the kinetic energy, in joules, of a baseball traveling at a speed of 40meters per second?
A) 5.8
B) 58
C) 232
D) 2,320

Answer 1

The kinetic energy, in joules, of a baseball traveling at a speed of 40 meters per second is 232 joules. To calculate using the function f(x) = 0.145x^2, plug 40 into the equation to get f(40) = 232 joules. Option C.

Step-by-step explanation:

The function f(x) = 0.145x^2 models the kinetic energy of a baseball in joules, where x is the baseball's speed in meters per second.

To find the kinetic energy of a baseball traveling at a speed of 40 meters per second, we plug x = 40 into the function:

f(40) = 0.145 × (40)^2

f(40) = 0.145 × 1600

f(40) = 232 joules

Therefore, the kinetic energy of the baseball when traveling at 40 m/s is 232 joules

Hence, the right answer is option C.

Answer 2

The kinetic energy of the baseball is 232 joules.

Step-by-step explanation:

Identify the relevant information:

The function for kinetic energy: f(x) = 0.145x^2

Speed of the baseball: x = 40 meters per second

Plug the speed into the function:

f(40) = 0.145 * 40^2

Calculate f(40) = 232 joules

Therefore, the kinetic energy of the baseball traveling at 40 meters per second is 232 joules.

Answer Choice Analysis:

A) 5.8: This is too low. The function is quadratic, so the energy increases more rapidly with increasing speed than a linear relationship.

B) 58: This is also too low for the quadratic relationship.

C) 232: This is the correct answer, calculated as shown above.

D) 2,320: This is too high. While the quadratic relationship increases with speed, it wouldn't reach this value for a speed of 40 meters per second.