To determine the relation between S1 and S2, we can use the equations of motion for a particle under constant acceleration. In this case, since the force acting on the particle is constant, the acceleration will also be constant.
The equation relating distance, initial velocity, time, and acceleration is:
S = ut + (1/2)at^2,
where S is the distance traveled, u is the initial velocity, t is the time, and a is the acceleration.
Since the particle travels for 40 seconds, we can divide the motion into two intervals: the first 20 seconds (S1) and the next 20 seconds (S2).
For the first interval (0 to 20 seconds):
S1 = u(20) + (1/2)a(20)^2 = 20u + 200a ...(1)
For the second interval (20 to 40 seconds):
S2 = u(20) + (1/2)a(20)^2 = 20u + 200a ...(2)
Comparing equations (1) and (2), we can see that S1 is equal to S2:
S1 = S2
Therefore, the relation between S1 and S2 is that they are equal.