The position of a moving car at time t is given by f(t) = at2 + bt + c, t 0, where a, b …

Question

The position of a moving car at time t is
given by f(t) = at2 + 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 [t1
, t2
] is
attained at the point :

Accepted Answer

Vav = $${{f\left( {{t_2}} \right) - f\left( {{t_1}} \right)} \over {{t_2} - {t_1}}}$$ = f'(t)

$$ \Rightarrow $$ $${{a\left( {t_2^2 - t_1^2} \right) - b\left( {{t_2} - {t_1}} \right)} \over {{t_2} - {t_1}}}$$ = 2$a$t + b

$$ \Rightarrow $$ a(t2 + t1) + b = 2at + b

$$ \Rightarrow $$ t = $${{{t_1} + {t_2}} \over 2}$$

Solutions · 1