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Grade 11IIT JEE Entrance Exam

A particle starts from rest and travels a distance s with uniform acceleration then it travels a distance 2s with uniform speed finally Travels a distance 3 years with uniform retardation and comes to rest if the complete motion of the particle a straight line then find the ratio of its average velocity to maximum velocity

Shailesh

9 Years agoGrade 11

1 Answer

Vikas TU

6 Years ago

Let a be the uniform acceleration.

v² - u² = 2 a S => S = v² / 2 a as u = 0.
final velocity = v = √(2 a S)
time taken to reach this velocity : t1 = (v - u ) / a = v / a = √(2S/a)

Now the particle moves with this velocity for distance 2 S.
so time taken t2 = 2 S / v = 2 S / √(2aS) = √(2 S / a)

Now the particle moves with a uniform deceleration - a3 for a distance 3 S.
time taken t3 to stop.
2 * a3 * 3 S = v² - u² here v = 0 and u = √(2 a S)
=> a3 = a / 3
=> t3 = - u /a3 = 3 √( 2 S / a)

total time duration = t = t1 + t2 + t3 = 5 * √(2 S / a)
total distance travelled : S + 2S + 3S =6 S

=> average speed = 3 / 5 * √(2 a S)
maximum speed = √(2 a S)

Ratio = 3/5

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