JEE PYQ: Application Of Derivatives Question 40
Question 40 - 2020 (06 Sep Shift 1)
The position of a moving car at time $t$ is given by $f(t) = at^2 + bt + c$, $t > 0$, 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:
(1) $(t_2 - t_1)/2$
(2) $a(t_2 - t_1) + b$
(3) $(t_1 + t_2)/2$
(4) $2a(t_1 + t_2) + b$
Show Answer
Answer: (3)
Solution
Average speed $= \frac{f(t_2) - f(t_1)}{t_2 - t_1} = a(t_1 + t_2) + b$. Instantaneous speed $f’(t) = 2at + b = a(t_1 + t_2) + b \Rightarrow t = \frac{t_1+t_2}{2}$.
BETA
