A 56.0-kg runner has a speed of 3.10 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
a) 1/2 m v^2
b) 4. Ke varies with the square
To find the runner's kinetic energy at one instant, we can use the formula for kinetic energy:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
Given:
Mass (m) = 56.0 kg
Velocity (v) = 3.10 m/s
(a) To find the runner's kinetic energy at this instant, we can substitute the given values into the formula:
KE = (1/2) * 56.0 kg * (3.10 m/s)^2
Calculating this expression gives us the answer for part (a). Let's calculate it:
KE = (1/2) * 56.0 kg * (3.10 m/s)^2
= 0.5 * 56.0 kg * 9.61 m^2/s^2
= 271.36 J
Therefore, the runner's kinetic energy at this instant is 271.36 J.
(b) If the runner doubles his speed to reach the finish line, we need to calculate the new kinetic energy. Let's denote the final kinetic energy as KEf.
Given that the runner's velocity doubles, the new velocity would be 2 * 3.10 m/s = 6.20 m/s.
To find the new kinetic energy (KEf), we can again use the formula for kinetic energy:
KEf = (1/2) * mass * velocity^2
Substituting the values into the formula, we get:
KEf = (1/2) * 56.0 kg * (6.20 m/s)^2
Calculating this expression gives us the answer for part (b). Let's calculate it:
KEf = (1/2) * 56.0 kg * (6.20 m/s)^2
= 0.5 * 56.0 kg * 38.44 m^2/s^2
= 1080.32 J
Therefore, the runner's kinetic energy changes from 271.36 J to 1080.32 J when he doubles his speed to reach the finish line.