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