A car of mass 500kg is travelling along a horizontal road. The engine of the car is working at a constant rate of 5kW. The total resistance of motion is constant and is 250N. What is the acceleration of the car when its speed is at 5m/s?
work/second in from engine = thrust force * speed = 5,000 n m/s = F * 5 m/s
so F= 1,000 N
so
1,000 - 250 = 750 N = m a = 5,000 a
a = 750/5000
Correct answer to this
To find the acceleration of the car, we can start by calculating the net force acting on the car using Newton's second law of motion, which states that the net force is equal to the mass of an object multiplied by its acceleration.
Step 1: Calculate the net force:
Net Force = Total force - Resistance force
Given:
Mass of the car (m) = 500 kg
Resistance force (R) = 250 N
Net Force = Total force - Resistance force
Step 2: Calculate the total force:
Total power = Engine power output
Given:
Engine power output = 5 kW
Power (P) = Work done per unit time
Since power = force × velocity, we can rewrite it as:
Force = Power / velocity
Force = 5,000 W (since 1 kW = 1,000 W)
Velocity (v) = 5 m/s
Total force (F) = Force = Power / velocity
Step 3: Calculate the acceleration:
Using Newton's second law:
Net Force = Mass × Acceleration
Substituting the values:
Net Force = F
Mass (m) = 500 kg
Acceleration (a) = ?
Net Force = Mass × Acceleration
Now, we can combine the equations:
Power / velocity = Mass × Acceleration
Let's plug in the values:
5,000 W / 5 m/s = 500 kg × Acceleration
Divide both sides by 500 kg:
(5,000 W / 5 m/s) / 500 kg = Acceleration
Simplifying:
1,000 m/s^2 = Acceleration
Therefore, the acceleration of the car when its speed is 5 m/s is 1,000 m/s^2.