a 1600-kg vehicle moves with a velocity of 19.5 m/s. calculate the power required to reduce the velocity to 3.20 m/s in 11.0 s
To calculate the power required to reduce the velocity of the vehicle, we need to use the formula for power:
Power = Force × Velocity
First, let's calculate the force required to change the velocity of the vehicle. The force required is given by Newton's second law:
Force = Mass × Acceleration
The acceleration can be calculated using the equation for average acceleration:
Acceleration = Change in velocity / Time
Now, let's calculate the change in velocity:
Change in velocity = Initial velocity - Final velocity
Substituting the given values:
Change in velocity = 19.5 m/s - 3.20 m/s = 16.3 m/s
Now, let's calculate the acceleration:
Acceleration = Change in velocity / Time = 16.3 m/s / 11.0 s = 1.48 m/s^2
Now, let's calculate the force:
Force = Mass × Acceleration = 1600 kg × 1.48 m/s^2 = 2368 N
Finally, let's calculate the power:
Power = Force × Velocity = 2368 N × 3.20 m/s = 7577.6 W
Therefore, the power required to reduce the velocity to 3.20 m/s in 11.0 s is 7577.6 W.
To calculate the power required to reduce the velocity of the vehicle, we need to use the formula for power, which is:
Power = (Force × Distance) ÷ Time
First, we need to find the force acting on the vehicle. We can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration:
Force = Mass × Acceleration
In this case, the acceleration is given by the change in velocity divided by the time taken:
Acceleration = (Final Velocity - Initial Velocity) ÷ Time
Let's calculate the acceleration:
Acceleration = (3.20 m/s - 19.5 m/s) ÷ 11.0 s
Acceleration = -16.3 m/s ÷ 11.0 s
Acceleration ≈ -1.482 m/s² (taking negative sign for deceleration)
Next, we can calculate the force acting on the vehicle:
Force = Mass × Acceleration
Force = 1600 kg × (-1.482 m/s²)
Force ≈ -2371.2 N (taking negative sign for opposite direction of motion)
Now, we can calculate the distance traveled by the vehicle during the deceleration:
Distance = Average Velocity × Time
Average Velocity = (Initial Velocity + Final Velocity) ÷ 2
Average Velocity = (19.5 m/s + 3.20 m/s) ÷ 2
Average Velocity = 22.7 m/s ÷ 2
Average Velocity ≈ 11.35 m/s
Distance = 11.35 m/s × 11.0 s
Distance ≈ 124.85 m
Finally, we can calculate the power required to reduce the velocity:
Power = (Force × Distance) ÷ Time
Power = (-2371.2 N × 124.85 m) ÷ 11.0 s
Power ≈ -26900.12 W
The power required to reduce the velocity of the vehicle to 3.20 m/s in 11.0 s is approximately -26900.12 Watts. The negative sign indicates that power is being expended or lost by the system.
decrease in kinetic energy = (1/2)(1600) (19.5^2 - 3.2^2) = 800(370) = 296,000 Joules
296,000 Joules/11 s = 26,900 watts
= about 27 kilowatts