Revision graphs of velocity, acceleration, displacement

Here's a revision of graphs for displacement, velocity, and acceleration:

• Displacement-Time Graph ($s-t$ graph):

  • This graph shows an object's position (displacement) over time.
  • The slope of the $s-t$ graph represents the object's velocity.
  • A straight line indicates constant velocity, while a curved line indicates changing velocity (acceleration).

• Velocity-Time Graph ($v-t$ graph):

  • This graph shows an object's velocity over time.
  • The slope of the $v-t$ graph represents the object's acceleration.
  • The area under the curve of the $v-t$ graph represents the object's displacement.
  • A horizontal line means constant velocity (zero acceleration), and a straight sloped line means constant acceleration.

• Acceleration-Time Graph ($a-t$ graph):

  • This graph shows an object's acceleration over time.
  • The area under the curve of the $a-t$ graph represents the change in velocity of the object.
  • A horizontal line indicates constant acceleration.

In summary:

$$\text{Slope of } s-t \text{ graph} = v$$ $$\text{Slope of } v-t \text{ graph} = a$$ $$\text{Area under } v-t \text{ graph} = \Delta s$$ $$\text{Area under } a-t \text{ graph} = \Delta v$$