A 1000 kg car can accelerate from rest to a speed of 25 m/s in 10 s. What average power must the engine of car produce in order to cause this acceleration? Neglect friction losses
First find k.E=1/2mv'2
K.e=1/2 1000x (25)2=
E=312500 j
Now
P=E/t
P=312500/10=31250
Now convert in kilo
31250/1000=31.25 thanks
To find the average power the engine of the car must produce to cause this acceleration, we need to use the work-energy principle. The work-energy principle states that the work done on an object is equal to its change in kinetic energy.
The work done on the car can be calculated using the formula:
Work = Force × Distance
In this case, the force causing the acceleration is the net force acting on the car, which can be calculated using Newton's second law:
Force = Mass × Acceleration
The distance traveled by the car during this acceleration can be calculated using the formula:
Distance = (1/2) × Acceleration × (Time^2)
The change in kinetic energy can be calculated using the formula:
Change in Kinetic Energy = (1/2) × Mass × (Final Velocity^2 - Initial Velocity^2)
Since the car starts from rest, the initial velocity is 0, so the change in kinetic energy simplifies to:
Change in Kinetic Energy = (1/2) × Mass × Final Velocity^2
Now, we can equate the work done on the car with the change in kinetic energy:
Force × Distance = (1/2) × Mass × Final Velocity^2
Since power is defined as the work done per unit time, we can divide both sides of the equation by the time taken (10 s) to find the average power:
Power = (Force × Distance) / Time
Power = [(Mass × Acceleration) × Distance] / Time
Now we can substitute the relevant values into the equation:
Mass = 1000 kg
Final Velocity = 25 m/s
Time = 10 s
First, we need to find the acceleration and the distance traveled during the acceleration.
Acceleration = (Final Velocity - Initial Velocity) / Time
= (25 m/s - 0) / 10 s
= 2.5 m/s^2
Distance = (1/2) × Acceleration × (Time^2)
= (1/2) × 2.5 m/s^2 × (10 s)^2
= 125 meters
Substituting the values:
Power = [(Mass × Acceleration) × Distance] / Time
= [(1000 kg × 2.5 m/s^2) × 125 meters] / 10 s
= 3125 watts
Therefore, the average power that the engine of the car must produce to cause this acceleration is 3125 watts.
Answer given by nazish is correct.
M*g = 1000 * 9.8 = 9800 N. = Wt. of car.
a = 25/10 = 2.5 m/s^2.
d = 0.5a*t^2 = 1.25*10^2 = 125 m.
P = F * d/t = 9800 * 125/10 = 122,500J/s = 122,500 Watts.