# Q 3.28  The velocity-time graph of a particle in one-dimensional motion is shown in the figure:                Which of the following formulae are correct for describing the motion of the particle over the time-interval t1 to t2 :(a)         $x(t_{2})=x(t_{1})+v(t_{2})(t_{2}-t_{1})+\frac{1}{2}a(t_{2}-t_{1})^{2}$(b)        $v(t_{2})= v(t_{1})+a (t_{2}-t_{1})$(c)     $v_{average }=\frac{\left [ x(t_{2})-v(t_{2}) \right ]}{(t_{2}-t_{1})}$(d)      $a_{average }=\frac{\left [ v(t_{2})-v(t_{2}) \right ]}{(t_{2}-t_{1})}$(e)         $x(t_{2})=x(t_{1})+v_{average}(t_{2}-t_{1})+\left ( \frac{1}{2} \right )a_{average}(t_{2}-t_{1})^{2}$(f)       $x(t_{2})-x(t_{1})$  =area under the v-t curve bounded by the time axis and the dotted line shown.

Only the formulae given in (c), (d) and (f) are correct for describing the motion of the particle over the time-interval tto t2.

The formulae given in (a), (b) and (e) are incorrect as from the slope of the graph we can see that the particle is not moving with constant acceleration.

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