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 32.0 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.

Answer 1

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.