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The velocity-time graph of a particle in one dimensional motion is shown in the figure. Which of the following formula is correct for describing the motion 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) \( x\left(t_{2}\right)=x\left(t_{1}\right)+v_{\text {average }}\left(t_{2}-t_{1}\right)+(1 / 2) a_{\text {average }}\left(t_{2}-t_{1}\right)^{2} \)
(f) \( x\left(t_{2}\right)-x\left(t_{1}\right)= \) area under the \( v-t \) curve bounded by the \( \mathrm{t} \)-axis and the dotted line shown.
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