Question

speedometer readings for a vehicle (in motion) at 5 - second intervals are given in the table.

t (sec)	0	5	10	15	20	25	30
v (ft/s)	0	9	32	57	73	70	52

estimate the distance traveled by the vehicle during this 30 - second period using ( l_6 ), ( r_6 ) and ( m_3 ).
( l_6 = ) (square) feet
( r_6 = ) (square) feet
( m_3 = ) (square) feet
question help: (square) video (square) message instructor
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Explanation:

Step1: Define interval width

$\Delta t = 5$ seconds

Step2: Calculate $L_6$ (left endpoints)

$L_6 = \Delta t \times (v(0)+v(5)+v(10)+v(15)+v(20)+v(25))$
$L_6 = 5 \times (0+9+32+57+73+70)$
$L_6 = 5 \times 241 = 1205$

Step3: Calculate $R_6$ (right endpoints)

$R_6 = \Delta t \times (v(5)+v(10)+v(15)+v(20)+v(25)+v(30))$
$R_6 = 5 \times (9+32+57+73+70+52)$
$R_6 = 5 \times 293 = 1465$

Step4: Calculate $M_3$ (midpoints, 3 intervals)

First, midpoints correspond to $t=5,15,25$ (interval width $\Delta t=10$)
$M_3 = 10 \times (v(5)+v(15)+v(25))$
$M_3 = 10 \times (9+57+70)$
$M_3 = 10 \times 136 = 1360$

Answer:

$L_6 = 1205$ feet
$R_6 = 1465$ feet
$M_3 = 1360$ feet