The velocity of a stone moving under gravity t seconds after being thrown up at

Question

The velocity of a stone moving under gravity t seconds after being thrown up at 35 ft/s is given by

v(t) = ?32t + 35 ft/sec.

Use a Riemann sum with 5 subdivisions to estimate

.

_____

What does the answer represent?

The answer represents the total change in position so, after 4 seconds, the stone is about _____ft below where it started.

4 v(t) dt 0 The velocity of a stone moving under gravity t seconds after being thrown up at 35 ft/s is given by v(t) = ?32t + 35 ft/sec. Use a Riemann sum with 5 subdivisions to estimate 4 v(t) dt Integral 0 . _____ What does the answer represent? The answer represents the total change in position so, after 4 seconds, the stone is about _____ft below where it started.

Explanation / Answer

v(t) = ?32t + 35 ft/sec.

Riemann sum for (0,4) with 5 subdivisions.

Interval =(0,4)

Delta x = 0.8

Riemann left sum =0.8(35+9.4-16.2-41.8-67.4) = -81

Riemann right sum = 0.8(9.4-16.2-41.8-67.4-93) =-218

Average of these two = -149.5

This is the integral value.

This is nothing but distance moved from 0 to 4 second. Negative sign represents the body moving down.

The answer represents the total change in position so, after 4 seconds, the stone is about __149.5___ft below where it started.

t 0 0.8 1.6 2.4 3.2 4 v 35 9.4 -16,2 -41.8 -67.4 -93

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