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
To calculate the acceleration of the car, we can use the power equation:
Power = force x velocity
Rearranging the equation, we have:
force = power / velocity
First, let's convert the speed from km/hr to m/s:
Speed = 49.7 km/hr = 49.7 x 1000 / 3600 m/s = 13.8 m/s
Now we can plug in the values into the equation:
Force = 4300.0 W / 13.8 m/s
Force = 311.594 W/m
Since force = mass x acceleration, we can rearrange the equation:
Acceleration = force / mass
Acceleration = 311.594 W/m / 900.0 kg
Acceleration = 0.346 m/s^2
Therefore, the acceleration of the car at that time is 0.346 m/s^2.
To calculate the acceleration of the car, we can use the equation for power:
Power = force x velocity.
We are given the power supplied by the engine (4300 W) and the velocity of the car (13.8 m/s). The force in this equation represents the net force acting on the car.
Power = force x velocity
4300 = force x 13.8
To calculate the force, we can rearrange the equation:
force = power / velocity
force = 4300 / 13.8
Now, we need to determine the force acting on the car. This force can be found by equating it to the product of the mass of the car and its acceleration:
force = mass x acceleration
Rearranging the equation to solve for acceleration:
acceleration = force / mass = (4300 / 13.8) / 900
Now we can substitute the values and calculate the acceleration:
acceleration = (4300 / 13.8) / 900
acceleration ≈ 0.357 m/s²
Therefore, the acceleration of the car at that time is approximately 0.357 m/s².