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 find the power exerted by the engine, we can use the formula: Power = Force x Velocity.
1. First, calculate the total resistance acting against the car as it travels up the slope: Resistance = Frictional force + Air resistance = 100 Newton.
2. Next, calculate the force required to overcome the resistance: Force = Mass x Acceleration. Since the car is moving at a constant speed up the slope, the net force is zero. Therefore, the force required to overcome resistance is equal to the gravitational force pulling the car downhill.
Gravitational force = Mass x Gravitational acceleration = Mass x 9.8 m/s².
In this case, the car is moving uphill, so the gravitational force is acting against the direction of motion.
3. Now calculate the power exerted by the engine: Power = Force x Velocity. Since force and velocity are in the same direction, we can use the absolute values.
Power = (Mass x 9.8) x (10 m/s) + 100 Newton x 10 m/s.
Calculate the values and you will get the answer in watts.
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To find the acceleration when the car is descending the same slope at a speed of 20m/s, we can use the formula: Power = Force x Velocity. But in this case, we are given the power, so we need to solve for the force.
1. Given power = 2 kW. Convert it to watts: 1 kW = 1000 watts.
Power = Force x Velocity ⟹ Force = Power / Velocity.
Calculate the value of force in Newton.
2. Once you have the force, you can use the formula Force = Mass x Acceleration to solve for acceleration.
Acceleration = Force / Mass.
Calculate the value of acceleration in m/s².
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To calculate how long it will take for the car to come to rest after the engine is shut off, you can use the equation: Final velocity = Initial velocity + (Acceleration x Time).
We know the final velocity is 0 m/s, the initial velocity is 25 m/s, and we need to find the time it takes. The acceleration is the same as calculated in the previous step.
Rearrange the equation: Time = (Final velocity - Initial velocity) / Acceleration.
Calculate the value of time in seconds.