Question

If a particle starts moving along x-axis from the origin with initial velocity $u=1m{s}^{-1}$ and acceleration $a=2m{s}^{-3}$, the relationship between displacement and time is
$x=ut+\frac{1}{2}a{t}^2=1\times t+\frac{1}{2}\times 2\times t^2=t+t^2$
Draw the displacement $\left(x\right)-time\left(t\right)$ graph.

Answer 1

$x=t+t^2,a=1,b=1,c=0$

vertex $t=-\frac{b}{2a}=-\frac{1}{2\times 1}=-\frac{1}{2}.$

At t=$-\frac{1}{2},x=-\frac{1}{4}$