A ball starts from rest at the initial position x; = 0. The ball has a constant acceleration of 2.4 m/s2. (a) Write
the position-time equation for the ball. (b) What is the
position of the ball at t = 1.0 s? (c) What is its position
at t = 2.0 s?

We want to get the motion equations of a ball, and we want to use them to find the position of the ball at different times.

The solutions are:

We know that the ball starts from rest (so the initial velocity is zero) from the position x = 0.

The ball has a constant acceleration of 2.4 m/s^2

Then the acceleration equation is:

A(t) = 2.4 m/s^2

To get the velocity equation we integrate, remember, the initial velocity is zero, so we don't have a constant of integration:

V(t) = (2.4 m/s^2)*t

To get the position equation we integrate again, and because the initial position is x = 0, we don't have a constant of integration:

P(t) = 0.5*(2.4 m/s^2)*t^2

a) The position equation is:

P(t) = (1.2 m/s^2)*t^2

b) The position of the ball at t = 1s is given by:

P(1s) =  (1.2 m/s^2)*(1s)^2 = 1.2m

The ball position at t = 1s is x = 1.2m

c) Similar to the above case:

P(2s) = (1.2 m/s^2)*(2s)^2 = 4.8 m

x = 4.8m

If you want to learn more, you can read:

link

layers of the earth affect the waves and these effects are seen on instruiments such as seimometers