What average power would a 1.20 multiply.gif 103-kg speedboat need to go from rest to 18.0 m/s in 4.79 s, assuming the water exerts a constant drag force of magnitude fd = 5.34 multiply.gif 102 N and the acceleration is constant?
To find the average power required for the speedboat, we first need to calculate the work done. The work done is equal to the change in kinetic energy.
Step 1: Find the change in kinetic energy.
The initial kinetic energy is zero (as the speedboat is at rest).
The final kinetic energy can be calculated using the formula: KE = 0.5 * m * v^2.
where m is the mass of the speedboat and v is its final velocity.
Plugging in the values, we have:
KE = 0.5 * (1.20 x 10^3 kg) * (18.0 m/s)^2
Step 2: Calculate the work done.
The work done (W) can be calculated using the formula: W = KE_final - KE_initial.
Since the initial kinetic energy is zero, the work done is equal to the final kinetic energy: W = KE_final.
Now, substitute the calculated value for KE_final into the equation.
Step 3: Find the average power.
Power (P) is defined as the work done divided by the time taken: P = W / t.
Here, the time taken is given as 4.79 s.
Substitute the calculated value of W into the equation and divide it by the given time.
Finally, multiply the answer by -1 to get the magnitude of the average power, since the question specifies the magnitude of the drag force (opposite direction).
The average power required for the speedboat is the answer obtained from the calculations.