Question

The motion of a particle moving along the y-axis is represented as $y=3\left(t-2\right)+5{\left(t-2\right)}^2$ . Identify the correct statement

• A. the initial $\left(t=0\right)$ velocity of the particle is $3m{s}^{-1}$
• B. the acceleration of the particle is $5m{s}^{-1}$
• C. the particle is at the origin at $t=2s$
• D. all of the above

Answer 1

Answer: (C)

We know that $\overrightarrow{v}=\frac{dy}{dt}$ & $\overrightarrow{a}=\frac{\overrightarrow{\mathrm{dv}}}{dt}$
$v=\frac{dy}{dt}=3+10\left(t-2\right)$
At $t=0$ velocity $v=-17m{s}^{-1}$
$a=\frac{dv}{dt}=10m{s}^{-2}$
$y=3\left(t-2\right)+5{\left(t-2\right)}^2$
At the value of $y$ will be $y=3\left(2-2\right)+5{\left(2-2\right)}^2$
therefore $y=0$