Understanding Freely Falling Bodies: The Relationship Between S and t^2

In summary, the slope of a S vs. t^2 graph for a freely falling body under gravity gives g/2 because of the kinematic equation s=0.5*gt^2. This equation relates position and acceleration for a particle with zero initial velocity, resulting in a linear relationship between S and t^2 with a slope of g/2.
  • #1
ritwik06
580
0
1.For a freely falling body under gravity:
1.Why does the slope of S vs. t^2 gives g/2? Why not g itself?
2.Does the graph exhibit linear relationship?

I have studied that the slope of a velocity time graphy gives the acceleration directly. Now when we make a graph for S vs. t^2 from a graph of velocity-time for a freely falling body. So why does the slope of the graph obtained gives g/2?
 
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  • #2
Think of the equation relating position and acceleration (kinematic equation) for a particle with zero initial velocity
 
  • #3
cristo said:
Think of the equation relating position and acceleration (kinematic equation) for a particle with zero initial velocity

s=0.5*gt^2

right??
 
  • #4
I got it! Thanks!
 

1. What is a freely falling body?

A freely falling body is an object that is only acted upon by the force of gravity. This means that there are no other external forces, such as air resistance or friction, affecting its motion.

2. How does the acceleration of a freely falling body change?

The acceleration of a freely falling body is constant and does not change. It is always equal to the acceleration due to gravity, which is approximately 9.8 meters per second squared.

3. What factors can affect the motion of a freely falling body?

The motion of a freely falling body can be affected by the mass of the object, the gravitational force acting on it, and any external forces such as air resistance or friction. The shape and density of the object may also play a role.

4. How does the height from which a body is dropped affect its motion?

The height from which a body is dropped does not affect its motion. As long as there are no external forces acting on the object, it will continue to accelerate at a constant rate until it reaches the ground.

5. Can a freely falling body ever reach a velocity of zero?

Yes, a freely falling body will eventually reach a velocity of zero when it reaches its maximum height. This is because at the highest point of its motion, the force of gravity is equal to the force of the object's inertia, causing it to momentarily stop before falling back down.

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