How to find the average velocity?

Question

Can't someone please explain to me how to do question 2c and 9e? Thanks!

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Answer 1 · 2017-09-25T03:07:00

The average velocity is the average rate of change which is also the slope of the secant line: #(x_2-x_1)/(t_2-t_1)#

Number 2
The first #3# seconds are from #t=0# to #t=3#

At #t=0#, position is #11#

and at #t=3#, position is #(3)^3-12(3)+11 = -16#

So the average velocity is

#((-16)-(11))/(3-0) = -27/3 = -9# #cm#/#s#

Number 9

#x=t^2-7t+12#

Velocity: #v = 2t-7#

The particle moves in the negative direction from #t=0# to #t = 3.5#

It starts at #x = 12# and changes direction when it get to #x = -0.25# (at #t = 3.5#
That distance is #12.25# #cm#

It then travels in the positive direction until it gets to #2#at #t = 5#).
That distance is #2.25#.

The total distance traveled is #12.25+2.25 = 14.5# #cm#

The average speed is #14.5/5 = 2.9# #cm#/#s#.