Chapter 1.

1.1 Problem Statement

2.5*rand(1,2)
2*$t0
{2,3}
rand(2,3)
rand(1,9)
$a0*$t*$t-$b*$t+$s0
($st-$s0)/$t
2*$a0
round(($b + $vavg)/$2a0,1)

The position of a particle moving in a straight line during a $t–second trip is cm. Find a time t at which the instantaneous velocity is equal to the average velocity for the entire trip.

1.2 Step 1

The average velocity, vavg, is the average rate of change of a position function s(t) over a time interval [t0, t1].

vavg is defined as

Question Sequence

Question 1.1

The average velocity of the given position function s(t) during the interval from t0 = 0 s to t1 = $t seconds is

s($t) = ktPlo8x7WLY= cm

s(0) = fb59X/mhrUU= cm

Incorrect
Correct

Question 1.2

vavg = /14Ao413H505SJO7 cm/s.

Correct.
Incorrect.

1.3 Step 2

Question 1.3

The formula for the instantaneous velocity of a particle at time t is found by differentiating the position function s(t).

cm

s'(t) = rhri7cQU6Zs=·t - iSba6t70dtA= cm/s

Correct.
Incorrect.

1.4 Step 3

Question 1.4

To find the time when the instantaneous velocity is equal to the average velocity, set s'(t) = vavg and solve for t.

s'(t) = vavg

$2a0·t-$b = $vavg

t = qjqZz1N+poo= seconds

(Rounded to one decimal place)

Correct.
Incorrect.