Motion

How to find velocity?

Derivative of position function

How to find velocity?

Slope of the s (position) graph

How to find velocity?

Estimate the v from the table of s (MTV)

How to find velocity?

Integral of a (acceleration)

How to find velocity?

Signed area of the “a” graph

How to find acceleration?

Derivative of velocity function

How to find acceleration?

Slope of the v graph

How to find acceleration?

Estimate the a from the table of v (MVT)

How to find acceleration?

Second derivative of position

How to find speed?

absolute value of velocity

How to find speed?

flip the v graph up over the x-axis

What are the 3 notations for position?

x, y, s

How to find total distance from t=a to t=b?

Integral of |v| from t=a to t=b

How to find total distance from t=a to t=b?

signed area of the graph |v| from t=a to t=b

How to find displacement from t=a to t=b (shortest distance between two points)?

Integral of v from t=a to t=b

How to find displacement from t=a to t=b (shortest distance between two points)?

signed area of the graph v from t=a to t=b

How to find displacement from t=a to t=b (shortest distance between two points)?

Displacement = distance if all values of v are all positive

How to find displacement from t=a to t=b (shortest distance between two points)?

b b

∫ v(t) dt= s(b) - s(a) → s(b) = ∫ v(t)dt + s(a)

a a

How to tell the direction of moving?

v>0: right or up

How to tell the direction of moving?

v<0: left or down

How to tell the direction of moving?

v=0: at rest

How to show “speed up” or “slow down”

Read the graph of |v|

How to show “speed up” or “slow down”

Increasing: speed up

How to show “speed up” or “slow down”

decerasing: slow down

How to show “speed up” or “slow down”

Compare the signs of v and a

a and v same sign: speed up

a and v different signs: slow down

How to find the time when it is farthest to the right (left)?

Find the abs max (min) of the position

How to tell a point is moving away/toward the origin?

Find the position of the point : left or right of origin

How to tell a point is moving away/toward the origin?

Find the sign of velocity: left or right

How to tell 2 points are moving away/ toward each other?

Find the position of the 2 points:

How to tell 2 points are moving away/ toward each other?

Find the sign of velocity of 2 points: left of right

How to tell 2 points are moving away/ toward each other?

Draw a sketch to draw conclusion

How to tell the point given will return to its original position?

Find the velocity, set it =0

How to tell the point given will return to its original position?

Find the positions of all the points whose v=0

How to tell the point given will return to its original position?

Plot all the points on a number line including the given point

How to tell the point given will return to its original position?

If the points are found out are on both sides of the given point, then it returns (using IVT)