If a particle at rest starts moving in a horizontal straight line with uniform acceleration, we can use the equations of motion to determine the ratio of the distance covered during the fourth and the third second.
Let's denote the acceleration of the particle as 'a', and we know that it is uniform. The initial velocity of the particle is zero since it starts from rest.
The equations of motion for uniformly accelerated linear motion are:
- v = u + at
- s = ut + (1/2)at^2
- v^2 = u^2 + 2as
where:
- u is the initial velocity (zero in this case),
- v is the final velocity,
- t is the time,
- s is the displacement, and
- a is the uniform acceleration.
We can find the values of velocity and displacement at the end of the third and fourth seconds using these equations.
At the end of the third second (t = 3):
Using equation 1, we can find the final velocity v: v = u + at v = 0 + a(3) v = 3a
Using equation 2, we can find the displacement s: s = ut + (1/2)at^2 s = 0 + (1/2)a(3)^2 s = (9/2)a
At the end of the fourth second (t = 4):
Using equation 1, we can find the final velocity v: v = u + at v = 0 + a(4) v = 4a
Using equation 2, we can find the displacement s: s = ut + (1/2)at^2 s = 0 + (1/2)a(4)^2 s = 8a
Now, let's calculate the ratio of the distance covered during the fourth and third seconds:
Ratio = Distance covered in the fourth second / Distance covered in the third second
Ratio = s (at t = 4) / s (at t = 3) Ratio = (8a) / ((9/2)a) Ratio = (16/9)
Therefore, the ratio of the distance covered during the fourth and the third second is 16/9 or approximately 1.78.