Question

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. $x\left(t_2\right)=x\left(t_1\right)+v\left(t_1\right)\left(t_2-t_1\right)+\left(\frac{1}{2}\right)a{\left(t_2-t_1\right)}^2$
• 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. $a_{\text{average }}=\frac{\left[v\left(t_2\right)-v\left(t_1\right)\right]}{\left(t_2-t_1\right)}$

Answer 1

Answer: (D)

In the given interval the slope of v-t graph (i.e. acceleration) neither constant nor uniform. Therefore relations (a), (b) and (c) are incorrect but (d) is correct.