Velocity time graph problem?.

May 13, 2018

See below

Explanation:

Sketch graph:

We are asked the show that the shaded region $20 \le t \le 26$

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

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

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

Using:

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

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

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

$\setminus \setminus \setminus \setminus \setminus = 25.5 m$

Shown.