Question

# The engine in an imaginary sports car can provide constant power to the wheels over a...

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 32.0 mph in time 1.20 s .

a) At full power, how long would it take for the car to accelerate from 0 to 64.0 mph ? Neglect friction and air resistance. Please Express your answer in seconds.

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 32.0 mph in time 1.20 s , how long would it take to go from zero to 64.0 mph ? Please express your answer in seconds.

first of all convert the unit mile per hour into meter per second.

32.0 mph = 14.3 m/s

64.0 mph = 28.6 m/s

(a) suppose the acceleration of the car = a m/s^2

use the expression -

v = u + a*t

the car starts from rest. so, u = 0

So we have -

14.3 = 0 + a*1.2

=> a = 14.3 / 1.2 = 11.92 m/s^2

Now, suppose the car takes time t sec, to achieve the velocity 64.0 mph (28.6 m/s).

so use the expression -

v = u + a*t

=> 28.6 = 0 + 11.92*t

=> t = 28.6 / 11.92 = 2.40 sec.

(b) In this also, we will have -

Acceleration, a = 11.92 m/s^2

And so, the required time to attain a velocity of 64.0 mph (28.6 m/s) = 2.40 s.