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Chapter 14: Problem 44

If the engine of a 1.5-Mg car generates a constant power of \(15 \mathrm{~kW},\) determine the speed of the car after it has traveled a distance of \(200 \mathrm{~m}\) on a level road starting from rest. Neglect friction.

Short Answer

Expert verified
The final speed of the car can be found by substituting the known values in the identified formula as described in Step 3.

Step by step solution

01

Calculate Energy Produced

Since, power is the rate of energy being produced or utilized i.e., Power = Energy / Time. Given that Power is 15 kW, we should first convert it from kW to Watt for calculation by multiplying by 1000, so Power = 15000 Watts. We know the car travelled for 200m and we need to find the time it takes. As we don't have the speed yet, we use another formula that links power, force and speed. Power = Force x Speed. Since there's no friction and the car is moving on a level road, the force being worked against is 0, the only force being worked is the force that makes the car in motion. Therefore, Power = Mass x Acceleration x Speed.
02

Calculate Acceleration

First, convert the mass of car into kg for calculation i.e 1.5-Mg car is 1500 kg. Now we can get the acceleration using our power and force equation where force is equal to mass times acceleration. Therefore, Acceleration = Power / (Mass x Speed). Since the car is starting from rest, initial speed = 0. We will have to find final speed which is also equal to average speed when starting from rest. Hence, Acceleration = Power / (Mass x Distance). Substituting the known values, Acceleration = 15000 Watts / (1500 kg x 200 m).
03

Calculate Final Speed

We know that Acceleration = Change in Speed / Time. Thus, Change in Speed = Acceleration x Time, which is the final speed since the car started from rest. We can find change in speed (Final Speed) from the kinematic equation derived from equations of motion which is: Final Speed^2 = Initial Speed^2 + 2 x Acceleration x Distance. Since the car is starting from rest, Initial Speed = 0. Hence, Final Speed = sqrt(2 x Acceleration x Distance). Substitute the values and solve to find the answer.

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Most popular questions from this chapter

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