The engine in an imaginary sports car can provide constant power to the wheels over a range of speeds from 0 to 70 miles per hour (mph). At

Question

The engine in an imaginary sports car can provide constant power to the wheels over a range of speeds from 0 to 70 miles per hour (mph). At full power, the car can accelerate from zero to 29.0mph in time 1.50s .

Part A

At full power, how long would it take for the car to accelerate from 0 to 58.0mph ? Neglect friction and air resistance. THE ANSWER IS “6 seconds” according the mastering physics.. BUT WHY???? Please show how you derive that answer…

Part B

A more realistic car would cause the wheels to spin in a manner that would result in the ground pushing it forward with a constant force (in contrast to the constant power in Part A). If such a sports car went from zero to 29.0mph in time 1.50s , how long would it take to go from zero to 58.0mph ?

Express your answer numerically, in seconds THE ANSWER IS 3 seconds. Please show how you derrive this answer!

Express your answer in seconds.

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Sigridomena 4 years 2021-08-31T16:58:19+00:00 1 Answers 7 views 0

Answers ( )

  1. binhan
    0
    2021-08-31T16:59:53+00:00
    Reply

    Answer:

    Part A

    it would take 6 sec

    it would take 3 sec

    Explanation:

    We are told that the power supplied to the wheel is constant which means that the sport car is gaining energy i.e

                               power \ \alpha \ energy

    Hence if power is constantly supplied energy constantly increase

    From the formula of the Kinetic energy

                           KE = \frac{1}{2} mv^2

    we can see that as the speed doubles from 29 mph  to 58 mph  the energy needed is 2^2 = 4 times of the energy from the formula

       Also the time needed would also be 4 times because energy i directly proportional to time

           Hence to reach 58mph the time that it would take is

                              = 4* 1.5sec = 6sec

         

    We are told that the ground pushes the car  with a constant force and

                     F = ma

    this means that the acceleration is also constant

                 now from newtons law

         v = u +at  

     Looking at it we see that final velocity is directly proportional with time

    hence it would take twice the time to reach twice the final velocity

            Time to reach 58mph = 3 s

            since time to reach 29 mph(\frac{1}{2} \ of \ [58mph]) =( \frac{1}{2} \ of \ 3sec )1.5 s

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