Verified Solution • 2025–26 Session moderate

QJEEM17Ph056c: JEE Main 2017 Physics - Class 11 JEEM17Ph056c Solution: A car is standing 200 m behind a bus, which is also at rest.…

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m/s2 and the car has acceleration 4 m/s2 . The car will catch up with the bus after a time of :

Multiple Choice Options

  • A 110 s\sqrt {110} \,s
  • B 120 s\sqrt {120} \,s
  • C 10  2 s10\,\,\sqrt 2 \,s
  • D 15 s

Step-by-Step Verified Solution

Acceleration of Car, aC = 4 m/s2

Acceleration of bus, aB = 2 m/s2

Initial distance between them, S = 200 m

Acceleration of Car with respect to bus,

aCB = aC −- aB = 4 −- 2 = 2 m/s2

As initially both are at rest so, uCB = 0

∴   \therefore\,\,\, S = UCB ×\times t + 12{1 \over 2} aCB ×\times t2

⇒\Rightarrow    \,\,\, 200 = 0 + 12{1 \over 2} ×\times 2 ×\times t2

⇒\Rightarrow    \,\,\, t2 = 200

⇒\Rightarrow    \,\,\, t = 10 2\sqrt 2 sec.

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