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I'm having trouble on finding how to solve this question that I received.

A 1500kg race car's engine can produce 150,000 Watts of power. Assuming the race car is able to convert 75% of the energy into kinetic energy, how fast could the car go in 8 seconds?

I understand that I have the mass, work (with efficiency), initial velocity, and time. I tried using the Energy formula (Ei +/- W = Ef). Using that I found the final velocity but how was I supposed to incorporate 8 seconds into it?

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  • $\begingroup$ Remember that power (Watts) has units of Energy / Time. This means that the amount of energy added to the race car depends on the amount of time the engine is running. Multiply the power by the time to get the amount of energy added to the car. $\endgroup$
    – Mike Flynn
    Apr 15, 2021 at 4:14

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Power is simply energy/time. Since 75% energy is converted to kinetic energy: $$ E = 150000W \times 8s \times 75/100 = 900000J $$ The formula for Kinetic energy is $1/2mv^2$. So equating the two expressions obtained: $$ 1/2mv^2 = 900000J; v^2 = 1800000J/1500kg = 1200m^2/s^2 $$ $$ v^2 = 1200m^2/s^2; v ≈ 34.64m/s $$ Good day!

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Well, power is just energy over time, one watt is just one joule/second. Hence, convert 150000w to Joules by canceling the seconds. --> 150000j/s * 8s = 1200000j Now you stated that 75% of the energy is converted to kinetic. so, --> 800000j now just solve for velocity using the definition of kinetic energy; (1/2)(m)(v^2) upon doing the algebra one fines that the car would be going 32.65m/s sigfigs(30m/s). Which is aproximatly 72mph sigfigs(67).

Also, have a great day =)

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  • $\begingroup$ Is not 75% of 1200000J = 900000J? $\endgroup$
    – Sid
    Apr 15, 2021 at 4:59
  • $\begingroup$ 75% of 12 is 9, but anyway please do not give complete answers to homework questions. We strive to help with conceptual problems so students can learn to do the work themselves. Thanks. $\endgroup$ Apr 15, 2021 at 5:32

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