6. An electric motor starts revving up, consuming energy according to the equati

Question

6. An electric motor starts revving up, consuming energy according to the equation W = C t^2 , where C = 200 J/s^2. (a) How long does it take for the engine to consume 1000 J of energy? (b) What is the equation giving the power output of the motor? (c) How long does it take for the motor to develop a power output of 1 hp? 7. The power required to move an object is P = K t^3, where t is the time and the constant K = 3 W/s^3. How much energy is required to move the object during the first 4 seconds?

Explanation / Answer

1) w=ct^2

t=sqrt(w/c)=sqrt(1000/200)

t=2.24 sec

2) power =dw/dt=2ct

3) p=2ct

t=p/2c=745.7/200=1.864 sec

4) p=kt^3

energy= integration of power

w=kt^4/4

w=3*4^4/4=192 J

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