The velocity-time graph of a particle in one-dimensional motion is shown in Figure.

Which of the following formulae are correct for describing the motton of the particle over the time-interval $t_1$ to $t_2$

$(a)$ $x\left(t_{2}\right)=x\left(t_{1}\right)+v\left(t_{1}\right)\left(t_{2}-t_{1}\right)+(1 / 2) a\left(t_{2}-t_{1}\right)^{2}$

$(b)$ $v\left(t_{2}\right)=v\left(t_{1}\right)+a\left(t_{2}-t_{1}\right)$

$(c)$ $v_{\text {average}}=\left(x\left(t_{2}\right)-x\left(t_{1}\right)\right) /\left(t_{2}-t_{1}\right)$

$(d)$ $a_{\text {average}}=\left(v\left(t_{2}\right)-v\left(t_{1}\right)\right) /\left(t_{2}-t_{1}\right)$

$(e)$ $x\left(t_{2}\right)=x\left(t_{1}\right)+v_{\text {average}}\left(t_{2}-t_{1}\right)+(2 / 2) a_{\text {average}}\left(t_{2}-t_{1}\right)^{2}$

$(f)$ $x\left(t_{2}\right)-x\left(t_{1}\right)=$ area under the $v -t$ curve bounded by the $t -$axis and the dotted line shown.

The following figures show velocity $v$ versus time $t$ curves. But only some of these can be realised in particle. These are :-

A bird flies for $4 \,s$ with a velocity of $|\;t – 2|\;m/s$ in a straight line, where $t$ is time in seconds. It covers a distance of ………$m$

The velocity time graph of a body moving in a straight line is shown in figure.The ratio of displacement to distance travelled by the body in time $0$ to $10\,s$ is