You know those velocity graphs or acceleration graphs and it says describe the motion of the particle at t=whatever? Can someone give me a run down on how to do that please!
Well if you need to describe the motion based off what you have.
Suppose you have the graph of the displacement.
Velocity is the first derivative of the displacement
Therefore if the graph is increasing, velocity is positive
If graph is decreasing, velocity is negative
If graph is at a stationary point, particle is at rest
Acceleration is the second derivative of the displacement
Therefore if the graph is concave up, acceleration is positive
If the graph is concave down, acceleration is positive
If we are at a point of inflexion, acceleration is constant (possibly 0 but we don't know).
And say we were given the graph of the velocity.
Velocity is the first derivative
Hence v > 0 means particle is travelling away from the origin (+'ve direction, to the right, however you memorised it)
v < 0 means particle is travelling in the other direction from the origin (-'ve direction, to the left etc.)
And those are just some examples. If you know what the derivatives actually MEAN then this is more intuitive than trying to rote learn a few dot points.