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  4. The velocity of a particle which starts from rest is given by the following table. t (in second) 0 2 4 6 8 10 v (in m/s) 0 12 16 20 35 60 The total distance travelled (in metre) by the particles in 10 s, using Trapezoidal rule is given by

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Q. The velocity of a particle which starts from rest is given by the following table.
t (in second) 0 2 4 6 8 10
v (in m/s) 0 12 16 20 35 60

The total distance travelled (in metre) by the particles in $10\, s$, using Trapezoidal rule is given by

EAMCETEAMCET 2009

Solution:

Given table is
t 0 2 4 6 8 10
v 0 12 16 20 35 60

Here, $h=\frac{10-0}{5}=2$
$\therefore $ Total distance $=\frac{h}{2}\left[f\left(x_{0}\right)+2\left\{f\left(x_{1}\right)+f\left(x_{2}\right)\right.\right.$
$\left.\left.+f\left(x_{3}\right)+f\left(x_{4}\right)\right\}+f\left(x_{5}\right)\right]$
$=\frac{2}{2}[0+2(12+16+20+35)+60]$
$=166+60=226$