Rate of Change Question3

In this page rate of change question3 we are going to see solution of some practice question of the worksheet.

Question 3:

The distance x meters traveled by a vehicle in time t seconds after the brakes are applied is given by x = 20 t - (5/3)t². Determine

(i) the speed of the vehicle (in km/hr) at the instant the brakes are applied and

(ii) the distance the car traveled before it stops.

Solution:

the distance x meters traveled by a vehicle in time t seconds

x = 20 t - (5/3)t²

 to find the speed of the vehicle

dx/dt = 20 (1) - (5/3)(2t)

         = 20 - (10 t/3)

the speed of the vehicle (in km/hr) at the instant the brakes are applied 

t = 0

         = 20 - (10(0)/3)

          = 20 - 0

velocity at t = 0   

           = 20 meter/seconds

to find velocity after the brakes are applied

                  = 20 meter/seconds

to convert this into km/hr we have to multiply it with the fraction 3600/1000

                  = (20 x 3600)/1000

                  = 72 km/hr