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Counter-Strike: Source (2004)

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The velocity-time graph of a particle in one-dimensional motion is shown in the figure. Which of the following formulae is correct for describing the motion of the particle over the time interval \( t_{1} \) to \( t_{2} \) ?
A \( \quad \mathrm{x}\left(\mathrm{t}_{2}\right)=\mathrm{x}\left(\mathrm{t}_{1}\right)+\mathrm{v}\left(\mathrm{t}_{1}\right)\left(\mathrm{t}_{2}-\mathrm{t}_{1}\right)+\left(\frac{1}{2}\right) \mathrm{a}\left(\mathrm{t}_{2}-\mathrm{t}_{1}\right)^{2} \)
B \( \quad \mathrm{v}\left(\mathrm{t}_{2}\right)=\mathrm{v}\left(\mathrm{t}_{1}\right)+\mathrm{a}\left(\mathrm{t}_{2}-\mathrm{t}_{1}\right) \)
C \( \quad \mathrm{v}_{\text {average }}=\frac{\left(\mathrm{x}\left(\mathrm{t}_{2}\right)-\mathrm{x}\left(\mathrm{t}_{1}\right)\right)}{\left(\mathrm{t}_{2}-\mathrm{t}_{1}\right)} \)
D \( \quad \mathrm{a}_{\text {average }}=\frac{\left(\mathrm{v}\left(\mathrm{t}_{2}\right)+\mathrm{v}\left(\mathrm{t}_{1}\right)\right)}{\left(\mathrm{t}_{2}-\mathrm{t}_{1}\right)} \)
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