Velocity time graph problem?.

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Answer 1 · 2018-05-13T22:23:13

See below

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Sketch graph:

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Shade required region:

We are asked the show that the shaded region $20 \leq t \leq 26$ $20<=t<=26$

$s = 0.375 t^{2} - 13 t + 202$ $s=0.375t^2-13t+202$

Area under graph from $t = 20 \to t = 26$ $t=20->t=26$ is the area of the trapezium.

$\frac{1}{2} (2 + 6.5) \cdot 6 = 25.5 m$ $1/2(2+6.5)*6=25.5m$

Using:

$s = 0.375 t^{2} - 13 t + 202$ $s=0.375t^2-13t+202$

Distance from $t = 20 \to t = 26$ $t=20->t=26$

$s = 0.375 {(26)}^{2} - 13 (26) + 202 - (0.375 {(20)}^{2} - 13 (20) + 202)$ $s=0.375(26)^2-13(26)+202-(0.375(20)^2-13(20)+202)$

$\ \ \ \ \ =25.5m$

Shown.