Problem: A body starts from rest with uniform acceleration and travels a distance of 9 is 525 of Total distance in last second of its journey. Find how much time body is in motion and how much distance travel is if it covers 6 metre in 1 second?

Solution:

Given:

- The body starts from rest.
- The body has a uniform acceleration.
- The distance travelled in the last second of the journey is 9/525 of the total distance.
- The body covers 6 metres in 1 second.

To find:

- The time for which the body is in motion.
- The total distance travelled by the body.

Assumptions:

- The acceleration is constant throughout the journey.
- The journey is in a straight line.

Approach:

- Use the equations of motion to find the time and distance travelled by the body.
- Use the given information to solve for the unknowns.

Equations of Motion:

- v = u + at
- s = ut + 1/2 at^2
- v^2 = u^2 + 2as

Calculation:

- Let the initial velocity of the body be u and the acceleration be a.
- Let the total distance travelled by the body be S and the time for which it is in motion be t.
- From the given information, we know that the distance travelled in the last second of the journey is 9/525 of the total distance. Therefore, the distance travelled in the last second is (9/525)S.
- We also know that the body covers 6 metres in 1 second. Therefore, the final velocity of the body is 6 m/s.
- Using the first equation of motion, we can find the time taken by the body to reach a velocity of 6 m/s:

v = u + at
6 = 0 + at
t = 6/a

- Using the third equation of motion, we can find the total distance travelled by the body:

v^2 = u^2 + 2as
(6)^2 = 0^2 + 2aS
S = 18/a

- Using the second equation of motion, we can find the distance travelled by the body in the last second of the journey:

s = ut + 1/2 at^2
s = 0(1) + 1/2 a(1)^2
s = 1/2 a

- From the given information, we know that (9/525)S = s. Substituting the values of S and s, we get:

(9/525)(18/a) = 1/2 a

- Solving for a, we get:

a = 7.5 m/s^2

- Substituting the value of a in the equations for t and S, we get:

t = 0.8 s
S = 24 m

Answer:

- The body is in motion for 0.8 seconds.
- The total distance travelled by the body is 24 metres.