1. The document discusses vertical projectile motion, where objects move up and down under the influence of gravity. 2. Objects in vertical projectile motion experience a constant downward acceleration of 9.8 m/s^2 due to gravity. The time it takes an object to rise is equal to the time it takes to fall back to the initial height. 3. Equations of motion can be used to solve problems involving vertical projectile motion relating to displacement, velocity, acceleration, and time. Position-time and velocity-time graphs are similar to constant acceleration motion and depend on the initial velocity and position coordinates chosen.

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3. Vertical projectile motion - 1D
Physics
Grade 12

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Projectiles
Projectiles are objects that move through the air. In vertical projectile motion we deal with
objects that fall under the influence of gravity and only vertically.
Objects that move up and down (vertical projectiles) on the Earth accelerate with a
constant acceleration g which is approximately equal to 9,8 m·s−2
directed downwards
towards the centre of the earth.

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Time symmetry
The time it takes an object to rise to its maximum height, is the same as the time it will take
to fall back to its initial height. The magnitude of the velocity will also be the same but the
direction will be reversed. This is known as time symmetry and is a consequence of uniform
gravitational acceleration.

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Equations of motion
We can use the following equations of motion to solve problems involving vertical projectile
motion.
⃗vf =⃗vi +⃗gt
Δ⃗x=
⃗vf −⃗vi
2
t
Δ⃗x=⃗vi t+
1
2
⃗gt2
⃗vf
2
= ⃗vi
2
+2⃗gΔ⃗x

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Graphs
Graphs for vertical projectile motion are similar to graphs for motion at constant acceleration.
Initial velocity upwards – Position-time graph and velocity-time graph

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Initial velocity zero Initial velocity downwards Position-time graph for initial
velocity zero or downwards

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Position-time graphs for object thrown upwards
If we choose the point from which the
object is thrown as the origin of our
coordinate system then the graph will
look like this:
If we choose to centre our coordinate
system at the point where the object
lands then the graph will look like this:

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Acceleration-time graph
This does not depend on the starting velocity or position of the object.

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