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1)A particle moving in straight line experience constant acceleration for 20 second after starting from rest.If it travels a distance S1 in the first 10 second and S2 in the next 10 seconds then what is the relation between S1 and S2.?
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1)A particle moving in straight line experience constant acceleration ...
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1)A particle moving in straight line experience constant acceleration ...
Given


  • Particle starts from rest

  • Particle experiences constant acceleration for 20 seconds

  • It travels a distance S1 in the first 10 seconds

  • It travels a distance S2 in the next 10 seconds



To find

Relation between S1 and S2

Solution


  • Let the acceleration of the particle be 'a'.

  • As the particle starts from rest, initial velocity, u = 0.

  • Final velocity, v = u + at = at (since u = 0)

  • Distance travelled in the first 10 seconds, S1 = ut + 1/2 at^2 = 0 + 1/2 a(10)^2 = 50a

  • Distance travelled in the next 10 seconds, S2 = ut + 1/2 at^2 = vat + 1/2 a(10)^2 = v(10) + 50a = 10at + 50a = 60a

  • From the above equations, we can see that S2 is directly proportional to a.

  • As the particle experiences constant acceleration for 20 seconds, acceleration 'a' is constant during the entire journey of 20 seconds.

  • Therefore, S2 is directly proportional to S1.

  • Hence, the relation between S1 and S2 is S2 = kS1, where k is a constant of proportionality.



Conclusion

The distance travelled by the particle in the first 10 seconds (S1) is directly proportional to the distance travelled by the particle in the next 10 seconds (S2). Therefore, the relation between S1 and S2 is S2 = kS1, where k is a constant of proportionality.
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1)A particle moving in straight line experience constant acceleration for 20 second after starting from rest.If it travels a distance S1 in the first 10 second and S2 in the next 10 seconds then what is the relation between S1 and S2.?
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