Weswork calculus n 13 anmadov/h0 4.2 measuhng HW 4.2 Measuring Distance from Vel

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Weswork calculus n 13 anmadov/h0 4.2 measuhng HW 4.2 Measuring Distance from Velocity: Problem 1 Preious Problem ist Next (1 point) A car comes to a stop six seconds after the driver applies the brakes. while th recorded: brakes are or, the folldwing velocities are Time since brakes applied ec2 4 velocity (t/s 100 51 180 Give lower and upper estimates (using all of the available data)tor the c istance the car traveled atter the braken were applied. lower upper for each, include units) On a sketch of velocity against time, show the lower and upper es imares you founl acov Note: You can eam partial credit on this probiem. Prevlew My Answers Submit Answers You have attempted this problem 2 times Your overall recorded score is 0%. You have unlimited attempts remaining Email Instructor

Explanation / Answer

The left sum will give an upper estimate and the right sum will give a lower estimate of the distance traveled since velocity is decreasing over the interval from t = 0 to t = 6

width = 6-0 / 3 => 6/3 => 2

divide the interval into 3 sub intervals

[ 0,2 ] , [ 2,4] , [ 4,6]

Left Sum = 2 [ v(0) + v(2) + v(4) ]

= 2 [ 100 + 51 + 18 ]

= 2 [ 169 ]

= 338 feet

Right Sum = 2 [ v(2) + v(4) + v(6) ]

= 2 [ 51 + 18 + 0 ]

= 2 [ 69 ]

= 138 feet

Therefore, the total distance the car traveled after the brakes were applied is between 138 ft and 338 ft

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