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.

Answer 1

Part A

it would take 6 sec

it would take 3 sec

Step-by-step 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 = (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(
`(1)/(2) \ of \ [58mph]`) =(
`(1)/(2) \ of \ 3sec` )1.5 s