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 $3 \, m \, s^{- 1}$
• B. the acceleration of the particle is $5 \, m \, s^{- 1}$
• C. the particle is at the origin at $t=2 \, s$
• D. all of the above

Answer 1

Answer: (C)

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