Question

A particle moves along $x-$axis in such a way that its $x-$ coordinate varies with time $t\left(\text{in s}\right)$ according to the equation: $x=(6-4t+6t^2)\text{m}$. The velocity of the particle will vary with time according to the graph

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$v=\frac{d}{dt}\left(x\right)=-4+12tm/s$
When $t=0\text{s},v=-4m/s$
When $v=0\frac{m}{s},12t=4$ or $t=\frac{4}{12}=\frac{1}{3}\text{s}$
Slope of $v-t$ graph,
$=\frac{v_2-v_1}{t_2-t_1}=\frac{0-(-4)}{\frac{1}{3}-0}=12$
(Positive slope)
Thus, option (a) is the correct answer.