A car of mass 1.2tonnes is travelling up a slope of 1 in 150 at a constant speed of 10m/s. if the frictional and air resistances are 100 newton , calculate the power exerted by the engine. the car descends the same slope working at a rate of 2kw what will be its acceleration when its speed is 20m/s if the resistances are the same? if the engine is shut off when the speed of the cat is 25m/s as it descends the slope, how long will it be before the car comes to test? I need the answer please
To calculate the power exerted by the engine, we need to find the total force acting against the car and then multiply it by the velocity of the car.
Step 1: Calculate the total force acting against the car:
The total force can be found by summing up the frictional force and the air resistance force.
Given:
- Frictional and air resistances = 100 Newtons
Total force = Frictional force + Air resistance force
= 100 Newtons + 100 Newtons
= 200 Newtons
Step 2: Calculate the power exerted by the engine:
Power = Force × Velocity
= 200 Newtons × 10 m/s
= 2000 Watt (or 2 kilowatts)
Therefore, the power exerted by the engine is 2 kilowatts.
Now, let's move on to the second part of the question.
When the car descends the same slope, the engine works at a rate of 2 kilowatts. We need to calculate the acceleration of the car when its speed is 20 m/s, assuming the resistances are the same.
Step 1: Calculate the total force acting against the car:
Again, we need to find the total force acting against the car, taking into account the resistances.
Total force = Frictional force + Air resistance force
= 100 Newtons + 100 Newtons
= 200 Newtons
Step 2: Calculate the acceleration of the car using the equation:
Power = Force × Velocity
Acceleration = Power / (mass × velocity)
Given:
- Power = 2 kilowatts = 2000 Watts
- Mass = 1.2 tonnes = 1200 kg
- Velocity = 20 m/s
Acceleration = 2000 Watts / (1200 kg × 20 m/s)
= 2000/24000
= 0.0833 m/s²
Therefore, the acceleration of the car when its speed is 20 m/s is 0.0833 m/s².
Now, let's move on to the final part of the question.
When the engine is shut off at a speed of 25 m/s as the car descends the slope, we need to calculate the time it takes for the car to come to rest.
Step 1: Calculate the deceleration of the car using the equation:
Deceleration = (Resistance force) / mass
Given:
- Resistance force = 200 Newtons
- Mass = 1200 kg
Deceleration = 200 Newtons / 1200 kg
= 0.167 m/s²
Step 2: Calculate the time using the equation:
Time = (Final velocity - Initial velocity) / Deceleration
Given:
- Initial velocity = 25 m/s
- Final velocity = 0 m/s
- Deceleration = 0.167 m/s²
Time = (0 m/s - 25 m/s) / -0.167 m/s²
= 25 m/s / 0.167 m/s²
≈ 149.7 seconds or approximately 150 seconds
Therefore, it will take approximately 150 seconds for the car to come to rest after the engine is shut off.
I hope this helps!