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 32.0mph in time 1.10s .A)At full power, how long would it take for the car to accelerate from 0 to 64.0mph ? Neglect friction and air resistance. =4.40sPart BA 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 32.0mph in time 1.10s , how long would it take to go from zero to 64.0mph ?am not sure how to do part B

Answer 1

a) 4.40 s

b) 2.20 s

Step-by-step explanation:

Given parameters are:

At constant power ,

initial speed of the car,
`v_0=0`

final speed of the car,
`v=32` mph

At full power,

initial speed of the car,
`v_0=0`

final speed of the car,
`v=64` mph

a)

At constant power,
`KE = (1)/(2) mv^2`

At full power,
`KE = (1)/(2) m(2v)^2`

So
`KE_f = 4KE_i`

So, time to reach 64 mph speed is 4 times more than the initial time

`t = 4*1.10 =4.40` s

b)

`v=v_0+at\\a=(v-v_0)/(t)=(32-0)/(1.1/3600)=104727.27`
`miles/hours^2`

For final 64 mph speed,

`v=v_0+at\\t=(v-v_0)/(a)=(64-0)/(104727.27) = 6.111*10^(-4)`
`hours` =
`6.111*10^(-4)*3600=2.20` s