A 65.0-kg runner has a speed of 5.20 m/s at one instant during a long-distance event. (a) what is the runner's kinetic energy at this instant? (b) if he doubles his speed to reach the finish line, by what factor does his kinetic energy change
87.88J
A 65.0-kg runner has a speed of 5.20 m/s at one instant during a long distance event (a) What is the runner’s kinetic energy at this instant? (b) If he doubles his speed to reach the finish line, by what factor does his kinetic energy change?
A 65.0 kg runner has a speed of 5.20 m/s at one instant during a long-distance event. What is the runner’s kinetic energy at this instant?
To solve this problem, we need to use the formula for calculating kinetic energy:
Kinetic energy (KE) = 1/2 * mass * velocity^2
(a) To find the runner's kinetic energy at the given instant, we can plug in the values into the formula:
Mass (m) = 65.0 kg
Velocity (v) = 5.20 m/s
KE = 1/2 * 65.0 kg * (5.20 m/s)^2
= 1/2 * 65.0 kg * 27.04 m^2/s^2
= 703.6 J (rounded to one decimal place)
Therefore, the runner's kinetic energy at this instant is 703.6 Joules.
(b) If the runner doubles his speed to reach the finish line, we need to calculate the new kinetic energy.
New velocity (v') = 2 * 5.20 m/s
= 10.40 m/s
Using the same formula for kinetic energy:
New KE = 1/2 * 65.0 kg * (10.40 m/s)^2
= 1/2 * 65.0 kg * 108.16 m^2/s^2
= 3524.8 J (rounded to one decimal place)
The runner's new kinetic energy is 3524.8 Joules.
To find the factor by which the kinetic energy changes, we can divide the new kinetic energy by the initial kinetic energy:
Factor = New KE / Initial KE
= 3524.8 J / 703.6 J
≈ 5 (rounded to the nearest whole number)
The runner's kinetic energy changes by a factor of approximately 5 when he doubles his speed.
(a) K.E. (1/2) M V^2 = ___ joules ?
(b) doubling V quadruples the kinetic energy.
You do the numbers.