A car of mass 900.0 kg accelerates away from an intersection on a horizontal road. When the car speed is 49.7 km/hr (13.8 m/s), the net power which the engine supplies is 4300.0 W (in addition to the extra power required to make up for air resistance and friction). Calculate the acceleration of the car at that time.
P=Fv=mav
a=P/mv=4300/900•13.8=0.35 m/s²
Well, it seems like the car is really putting the pedal to the metal! Let's calculate its acceleration, shall we?
We know that net power is given by the equation:
Net Power = force x velocity
And since power is also given by the equation:
Power = force x velocity,
we can rearrange the equation to solve for force:
Force = Power / velocity
Now, we can use Newton's second law of motion, which states that:
Force = mass x acceleration
By substituting the equation for force into Newton's second law of motion, we can find the acceleration:
Acceleration = Force / mass
So, plugging in the values we have:
Acceleration = (Power / velocity) / mass
Acceleration = (4300.0 W / 13.8 m/s) / 900.0 kg
Acceleration ≈ 0.3663 m/s²
So, the car is accelerating at approximately 0.3663 m/s² at that time. Keep those wheels turning and stay safe out there!
To calculate the acceleration of the car, we can use the formula for power:
Power = force x velocity
We can rearrange this formula to solve for force:
Force = Power / velocity
Given that the power supplied by the engine is 4300.0 W and the velocity is 13.8 m/s, we can calculate the force:
Force = 4300.0 W / 13.8 m/s
Force = 311.594 N
Since force equals mass times acceleration, we can rearrange this equation to solve for acceleration:
Acceleration = Force / mass
Given that the mass of the car is 900.0 kg, we can calculate the acceleration:
Acceleration = 311.594 N / 900.0 kg
Acceleration ≈ 0.3462 m/s²
Therefore, the acceleration of the car at that time is approximately 0.3462 m/s².
To calculate the acceleration of the car, we can use the following equation:
Power = Force * Velocity
First, let's convert the speed from km/hr to m/s:
49.7 km/hr = 49.7 * (1000 m/1 km) * (1 hr/3600 s) = 13.8 m/s
Now we can rearrange the equation to solve for the force:
Force = Power / Velocity
Force = 4300.0 W / 13.8 m/s = 311.594 W/s
Since force equals mass times acceleration (F = m * a), we can rearrange the equation to solve for acceleration:
Acceleration = Force / Mass
Acceleration = 311.594 N / 900.0 kg = 0.3462 m/s^2
Therefore, the acceleration of the car at that time is 0.3462 m/s^2.