A car X moving of mass 500kg accelerates at 1m/s2 when the force due to the engine is 600N.
Starting from rest, a car of mass 1000kg accelerates steadily to 20m/s in 10 secs. What is the average power developed
2. V = Vo +a*t
20 = 0 + a*10,
a = 2 m/s^2.
F = M*a = 1000 * 2 = 2,000 N.
P = F*V/2 = 2000 * 20/2 = 20,000J/s = 20,000 Watts.
To find the average power developed by the car, we can use the equation for power:
Power = Work / Time
Since the car is accelerating steadily, we can calculate the work done using the formula:
Work = Force * Distance
First, let's find the force acting on the car. We can use Newton's second law of motion:
Force = Mass * Acceleration
Given:
Mass of the car (m) = 1000 kg
Acceleration (a) = (Change in velocity) / (Change in time) = (20 m/s - 0 m/s) / (10 s) = 2 m/s^2
So, the force acting on the car is:
Force = 1000 kg * 2 m/s^2 = 2000 N
Now, let's find the distance traveled by the car using the equation of motion:
Distance = (Initial velocity * Time) + (1/2 * Acceleration * Time^2)
Given:
Initial velocity (u) = 0 m/s
Time (t) = 10 s
Acceleration (a) = 2 m/s^2
Substituting the values:
Distance = (0 m/s * 10 s) + (1/2 * 2 m/s^2 * (10 s)^2)
Distance = 0 m + 1/2 * 2 m/s^2 * 100 s^2
Distance = 100 m
Now, we can calculate the work done:
Work = Force * Distance
Work = 2000 N * 100 m
Work = 200,000 Nm or 200,000 J (joules)
Finally, we can calculate the average power developed:
Average Power = Work / Time
Average Power = 200,000 J / 10 s
Average Power = 20,000 W (watts)
So, the average power developed by the car is 20,000 watts.
To find the average power developed by the car, we need to use the formula:
Average Power = Work Done/Time
In this case, the work done can be calculated using the equation:
Work Done = Force × Distance
First, we need to find the force applied to the car using Newton's second law of motion:
Force = mass × acceleration
Given:
Mass of the car (m) = 1000 kg
Acceleration (a) = (change in velocity)/(change in time) = (20 m/s - 0 m/s)/10 s = 2 m/s^2
Using the formula:
Force = 1000 kg × 2 m/s^2 = 2000 N
Now, let's find the distance traveled by the car:
Distance = (1/2) × acceleration × time^2
Distance = (1/2) × 2 m/s^2 × (10 s)^2 = 100 m
Now, we can calculate the work done:
Work Done = Force × Distance = 2000 N × 100 m = 200,000 J (Joules)
Finally, we can calculate the average power:
Average Power = Work Done/Time = 200,000 J / 10 s = 20,000 W (Watts)
Therefore, the average power developed by the car is 20,000 Watts.