Speedometer readings for a vehicle (in motion) at 10-second intervals are given in the table.

Question

Speedometer readings for a vehicle (in motion) at 10-second intervals are given in the table.

t (sec)	0	10	20	30	40	50	60
v (ft/s)	0	9	31	56	71	68	50

Estimate the distance traveled by the vehicle during this 60-second period using ,  and .

I do not even know where to start...am I using 6 rectangles for 6 or finding the upper and/or lower approximations for L and then multiplying by 6?

Answer 1

Just calculate the areas of the rectangles. Always sketch the picture, it will help immensely.

L6 = 10(0+9+31+56+71+68)

R6 = 10(9+31+56+71+68+50)

M3 = 20(9+56+68)

Answer 2

hi,

it is true you find 6 rectangles that width all rectangles are 10

when you want to find left,in fact the first rectangle is 10 x 0 and second will be 10 x 9 and so on

an important point is until 40 function is increasing then decreasing, so be care full when you need to find area of rectangle as result:

left = 10 (0 + 9+ 31 + 56 + 71 + 68) = 2992

when you need to find right the first rectangle is 10 x 9 and second is 10 x 31 and so on but last one will be 10 x 50

right = 10( 9 + 31 + 56 + 71 + 68 + 50 ) = 2850 be care full you have 6 rectangles

midpoints are (0 + 10) /2 , (10 + 20 )/2 and so on the last midpoint is (50 + 60 )/2

calculate area of trapezoids = 10/2 (( f₅ + f₁₅) + (f₁₅ + f₂₅) + (f₂₅ + f₃₅) +(f₃₅ +f₄₅) + (f₄₅ +f₅₅ ))

replace f_{5 =4.5} f₁₅ = 20 f₂₅= _43.5 f₃₅ = 63.5 f₄₅= 69.5 f₅₅ =59

find M₆

_{I hope it is useful,}

_Minoo