A car moves round a circular test track of radius 25m, making 36 complete revolutions every minute.
a. (i) Calculate the period of one revolution.
b. (ii) Show algebraically that the speed v of the car can be expressed in the form v=2πrf, where f is the frequency of revolution.
c. (iii) Using the result of part (ii), find the speed of the car in m/s and in km/h.
d. (iv) If the driver increases the number of revolutions per minute to 54 while keeping to the same track, what will be the new speed?