Verified Solution • 2025–26 Session moderate

QJEEM20Ma6054: JEE Main 2020 Mathematics - Class 12 JEEM20Ma6054 Solution: The position of a moving car at time t is given by f(t) = at 2…

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 :

Multiple Choice Options

  • A (t1+t2)2{{\left( {{t_1} + {t_2}} \right)} \over 2}
  • B (t2−t1)2{{\left( {{t_2} - {t_1}} \right)} \over 2}
  • C 2a(t1 + t2) + b
  • D a(t2 – t1) + b

Step-by-Step Verified Solution

Vav = f(t2)−f(t1)t2−t1{{f\left( {{t_2}} \right) - f\left( {{t_1}} \right)} \over {{t_2} - {t_1}}} = f'(t)

⇒\Rightarrow a(t22−t12)−b(t2−t1)t2−t1{{a\left( {t_2^2 - t_1^2} \right) - b\left( {{t_2} - {t_1}} \right)} \over {{t_2} - {t_1}}} = 2 aa t + b

⇒\Rightarrow a(t2 + t1) + b = 2at + b

⇒\Rightarrow t = t1+t22{{{t_1} + {t_2}} \over 2}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring