Motion

How to find velocity

a. Derivative of a function

b. Slope of the s graph

c. Estimate the v from the table of s (MVT)

d. integral of a

e. Signed area of the “a” graph

f. integral of acceleration plus v(a)

How to find acceleration?

a. derivative of velocity function

b. slope of the v graph

c. estimate the a from the table of v (MVT)

d. second derivative of position

How to find speed?

a. absolute value of velocity

b. flip the v graph up over the x-axis

How to find total distance?

a. integral of |v| from t=a to t=b

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

How to find displacement (shortest distance between two points)?

a. integral of v from t=a to t=b

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

How to find position s(b) given v and point x(a)?

integral of v(t) from a to b and integral of v(t) from a to b + s(a)

How to tell direction?

a. v>0: right up

b. v<0: left or down

c. v=0: at rest, not moving

How to do “speed up, slow down”?

a. read the graph of |v|

• increasing: speed up

• decreasing: speed down

b. compare the signs of v and a

• a and v same sign: speed up

• a and v different sign: slow down

How to find farthest to the right (left)

find the abs max (min) of the position

How to tell a pt is moving away or toward the origin

a. find the position of the point: left or right of origin

b. find the sign of velocity: left or right

how to tell 2 pts are moving away or toward

a, find the position of the 2 points:

b. find the sign of velocity of 2 points: left or right

c. draw a sketch to draw conclusion

how to tell the given point will return to the original

a. find velocity, set it = 0, find these points

b. plot all the points on a number line including the given point

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