A 59 kg sprinter, starting from rest, runs 47 m in 7.0 s at constant acceleration.?
What is the sprinter's power output at 2.0 s, 4.0 s, and 6.0 s?
Instantaneous Power is the force times velocity
P = Fv
Because the acceleration is constant, the force will be constant as well
F = ma
P = mav
for constant acceleration, the velocity at each time is found using
v = at
P = ma(at) = ma²t
find the acceleration using kinematic equation
s = ½at²
a = 2s/t²
a = 2(47) / 7.0²
a = 1.918 m/s²
P(2.0) = 59(1.918²)2.0 = 434.25 W = 0.43 kW
P(4.0) = 59(1.918²)4.0 = 868.51 W = 0.87 kW
P(6.0) = 59(1.918²)6.0 = 1302.76 W = 1.3 kW
I hope this helped.
