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.