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The velocity-time graph of a \( v \uparrow \) particle in one-dimensional
\( \mathrm{P} \) motion is shown in the figure.

W Which of the following formulae is correct for describing the motion of the particle over the time interval \( t_{1} \) to \( t_{2} \) ?
(a) \( x\left(t_{2}\right)=x\left(t_{1}\right)+v\left(t_{1}\right)\left(t_{2}-t_{1}\right)+\left(\frac{1}{2}\right) a\left(t_{2}-t_{1}\right)^{2} \)
(b) \( v\left(t_{2}\right)=v\left(t_{1}\right)+a\left(t_{2}-t_{1}\right) \)
(c) \( v_{\text {average }}=\frac{\left(x\left(t_{2}\right)+x\left(t_{1}\right)\right)}{\left(t_{2}-t_{1}\right)} \)
(d) \( a_{\text {average }}=\frac{\left(v\left(t_{2}\right)-v\left(t_{1}\right)\right)}{\left(t_{2}-t_{1}\right)} \)
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