A 59.0-kg runner has a speed of 3.20 m/s at one instant during a long-distance event.

(a) What is the runner's kinetic energy at this instant?
KEi = J

(b) If he doubles his speed to reach the finish line, by what factor does his kinetic energy change?
KEf
KEi
=

KE= 1/2 m v^2

what happens of you double v?

(a) To find the runner's kinetic energy at this instant, we can use the formula:

KE = 1/2 * m * (v^2)

Where:
KE is the kinetic energy
m is the mass of the runner (59.0 kg)
v is the speed of the runner (3.20 m/s)

Substituting the given values into the formula, we get:

KE = 1/2 * 59.0 kg * (3.20 m/s)^2

Simplifying the equation:

KE = 1/2 * 59.0 kg * 10.24 m^2/s^2

KE = 307.52 J

Therefore, the runner's kinetic energy at this instant is 307.52 Joules (J).

(b) To find the factor by which his kinetic energy changes when he doubles his speed, we can use the formula:

Factor of change = KEf / KEi

Where:
KEf is the kinetic energy after doubling the speed
KEi is the initial kinetic energy (307.52 J)

Since the speed is doubled, the final speed is 2 * 3.20 m/s = 6.40 m/s.

Using the formula for kinetic energy:

KEf = 1/2 * 59.0 kg * (6.40 m/s)^2

Simplifying the equation:

KEf = 1/2 * 59.0 kg * 40.96 m^2/s^2

KEf = 1211.04 J

Now we can calculate the factor of change:

Factor of change = KEf / KEi

Factor of change = 1211.04 J / 307.52 J

Factor of change ≈ 3.94

Therefore, when the runner doubles his speed, his kinetic energy changes by a factor of approximately 3.94.

To find the answers to these questions, we need to use the equation for kinetic energy:

Kinetic energy (KE) = 0.5 * mass * velocity^2

(a) What is the runner's kinetic energy at this instant?

Given:
Mass of the runner (m) = 59.0 kg
Velocity of the runner (v) = 3.20 m/s

Using the formula for kinetic energy:
KE = 0.5 * m * v^2

Substituting the given values:
KE = 0.5 * 59.0 kg * (3.20 m/s)^2

Calculating the value:
KE = 0.5 * 59.0 kg * 10.24 m^2/s^2
KE = 306.88 J

Therefore, the runner's kinetic energy at this instant is 306.88 Joules (J).

(b) If he doubles his speed to reach the finish line, by what factor does his kinetic energy change?

Let's first calculate the new speed by doubling the initial speed:
v_new = 2 * v = 2 * 3.20 m/s = 6.40 m/s

Now, we can find the new kinetic energy using the formula for kinetic energy:
KE_new = 0.5 * m * v_new^2

Substituting the values:
KE_new = 0.5 * 59.0 kg * (6.40 m/s)^2

Calculating the value:
KE_new = 0.5 * 59.0 kg * 40.96 m^2/s^2
KE_new = 1211.84 J

Therefore, the runner's new kinetic energy is 1211.84 Joules (J).

Now, let's find the factor by which the kinetic energy changes:
Factor = KE_new / KE_initial

Substituting the values:
Factor = 1211.84 J / 306.88 J

Calculating the value:
Factor = 3.95

Therefore, the runner's kinetic energy changes by a factor of 3.95.