a car of mass 800kg attains a speed of 25m/s in a second.calculate the power developed in the engine
energy = 1/2 m v^2
energy / time = power
To calculate the power developed in the car's engine, we need to use the formula for power:
Power = Force x Velocity.
Since we're dealing with a car, we can assume that the force acting on the car is due to the engine's propulsion, and it can be calculated using Newton's second law of motion:
Force = Mass x Acceleration.
In this case, the mass of the car is given as 800kg, and the speed it attains is 25m/s in a second. To find the acceleration, we can use the kinematic equation:
v = u + at,
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Here, the initial velocity is assumed to be zero since it starts from rest.
Rearranging the equation to find the acceleration:
a = (v - u) / t.
Substituting the values:
a = (25m/s - 0m/s) / 1s = 25m/s^2.
Now that we have the acceleration, we can calculate the force:
Force = Mass x Acceleration = 800kg x 25m/s^2 = 20,000N.
Finally, we can substitute the force and velocity into the power formula:
Power = Force x Velocity = 20,000N x 25m/s = 500,000 Watts (or 500 kW).
So, the power developed in the engine is 500 kW.