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.?

Question

Answer

Answer

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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