Question

The velocity-time graph of a particle in one-dimensional motion is shown in figure. Which of the following formulae are correct for describing the motion of the particle over the time interval $t_1$ to $t_2.$



(i) $x\left(t_2\right)=x\left(t_1\right)+v\left(t_1\right)\left(t_2-t_1\right)+\frac{1}{2}a{\left(t_2-t_1\right)}^2$

(ii) $v\left(t_2\right)=v\left(t_1\right)+a\left(t_2-t_1\right)$

(iii) $v_{av}=\left[\frac{x\left(t_2\right)-x\left(t_1\right)}{\left(t_2-t_1\right)}\right]$

(iv) $a_{av}=\frac{\left[v\left(t_2\right)-v\left(t_1\right)\right]}{\left(t_2-t_1\right)}$

(v) $x\left(t_2\right)=x\left(t_1\right)+v_{av}\left(t_2-t_1\right)+\frac{1}{2}{a}_{av}{\left(t_2-t_1\right)}^2$

(vi) $x\left(t_2\right)-x\left(t_1\right)=$ Area under $v-t$ curve bounded by the $t$ -axis and the dotted line shown

• A. (iii) and (vi)
• B. (iii), (iv) and (vi)
• C. (ii), (iii) and (iv)
• D. (iv) and (vi)

Answer 1

Answer: (B)

The slope of the given graph over the time interval $t_1$ to $t_2$ is not constant and is not uniform. It means acceleration is not constant and is not uniform, therefore relations (a), (b) and (e) are not correct which is for uniform accelerated motion, but relations (c), (d) and (f) are correct, because these relations are true for both uniform or non-uniform accelerated motion.