A car of mass 860.0 kg accelerates away from an intersection on a horizontal road. When the car speed is 39.6 km/hr (11.0 m/s), the net power which the engine supplies is 5700.0 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.
power=work/time=force*velocity
solve for force.
then acceleration=force/mass
To calculate the acceleration of the car, we can use the formula:
Power = Force × Velocity
Given that the net power supplied by the engine is 5700.0 W, and the velocity of the car is 11.0 m/s, we can rearrange the formula to solve for the force:
Force = Power / Velocity
Substituting the given values, we have:
Force = 5700.0 W / 11.0 m/s
Now, to find the acceleration, we can use Newton's second law of motion, which states that:
Force = Mass × Acceleration
Rearranging the formula to solve for acceleration, we have:
Acceleration = Force / Mass
Substituting the values we found earlier, we have:
Acceleration = (5700.0 W / 11.0 m/s) / 860.0 kg
Now, we can calculate the acceleration:
Acceleration ≈ 0.681 m/s²
Therefore, the acceleration of the car at that time is approximately 0.681 m/s².