The position of a moving car at time t is given by f ( t ) = a t 2 + b t + c , t > 0 , where a , b and c are real numbers greater than 1 . Then the average speed of the car over the time interval t 1 , t 2 is attained at the point:

Step-by-step solution

Given: position of the moving car at time t   is   = f t = a t 2 + b t + c So, v avg = f t 2 - f t 1 t 2 - t 1 ⇒ v avg = a t 2 2 - t 1 2 + b t 2 - t 1 t 2 - t 1 ⇒ v avg = a t 1 + t 2 + b The instantaneous speed is given by: f ' t = 2 a t + b So, to get the point where average speed is equal to car's actual speed, f ' t = v avg ⇒ a t 1 + t 2 + b = a t + b ⇒ t = t 1 + t 2 2