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  4. Position of a particle moving along x-axis is given by x=2+8 t-4 t2. The distance travelled by the particle from t=0 to t=2 is :

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Q. Position of a particle moving along $x$-axis is given by $x=2+8 t-4 t^{2}$. The distance travelled by the particle from $t=0$ to $t=2$ is :

Motion in a Straight Line

Solution:

Area of $( v - t )$ curve $=$ displacements
$x =2+8 t -4 t ^{2}$
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$v=\frac{d x}{d t}=8-8 t$
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Distance travelled from $t =0$ to $t =2\, \sec$
$=\frac{1}{2} \times 1 \times 8+\frac{1}{2} \times 1 \times 8=4+4=8\, m$