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 displacement-time graph for two particles $A$ and $B$ is as follows. The ratio $\frac{v_A}{v_B}$ is

The speed-time graph of a particle moving along a fixed direction is shown in Figure Obtain the distance(in $m$) traversed by the particle in $m$ between $t=0\; s$ to $10\; s$

A particle moves along $X-$axis in such a way that its coordinate $X$ varies with time $t$ according to the equation $x = (2 – 5t + 6{t^2})\,m$. The initial velocity of the particle is…….$m/s$