a car of mass 1214.5 kg is moving at a speed of 62.5 mph when it misses a curve in the road and hits a bridge filling. If althe car comes to rest in 0.236 s, How much average power (in watts) is expended in this interval
62.5 mi/hr = 27.94m/s
power = energy/time = (1/2 mv^2)/time = 1214.5/2 * 27.94^2 / 0.236 W
To find the average power expended during this interval, we can use the work-energy principle. The work done on an object can be calculated as the change in kinetic energy.
The formula for kinetic energy is given by:
KE = (1/2) * mass * velocity^2
The change in kinetic energy is calculated as:
ΔKE = KE_final - KE_initial
Given:
Mass of the car (m) = 1214.5 kg
Initial velocity (v_initial) = 62.5 mph
Final velocity (v_final) = 0
Time interval (Δt) = 0.236 s
First, let's convert the initial velocity from mph to m/s:
v_initial (m/s) = 62.5 mph * 0.447 m/s
v_initial (m/s) = 27.89 m/s
Now, let's calculate the initial kinetic energy:
KE_initial = (1/2) * m * v_initial^2
KE_initial = (1/2) * 1214.5 kg * (27.89 m/s)^2
KE_initial ≈ 473,234.718 J
Since the car comes to rest, the final kinetic energy is zero:
KE_final = 0 J
The change in kinetic energy is then:
ΔKE = KE_final - KE_initial
ΔKE = 0 J - 473,234.718 J
ΔKE = -473,234.718 J
Therefore, the work done on the car is negative because the car is decelerating.
Now, let's calculate the average power:
Average Power = Work / Time
Average Power = ΔKE / Δt
Average Power = (-473,234.718 J) / 0.236 s
Average Power ≈ -2,006,130.9 W
Therefore, the average power expended during this interval is approximately -2,006,130.9 Watts. The negative sign indicates that the power is being dissipated or released.