14. A particle moves along the $x$-axis so that its position at time $t$ is given by $x ( t ) = t ^ { 2 } - 6 t + 5$. For what value of $t$ is the velocity of the particle zero?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

A point P moving on the coordinate plane has position $( x , y )$ at time $t$ $(t > 0)$ given by $$x = t - \frac { 2 } { t } , \quad y = 2 t + \frac { 1 } { t }$$ What is the speed of point P at time $t = 1$? [3 points]
(1) $2 \sqrt { 2 }$
(2) 3
(3) $\sqrt { 10 }$
(4) $\sqrt { 11 }$
(5) $2 \sqrt { 3 }$

159. According to the position–time graph below, the motion of the particle is uniform. The speed of the particle at moment $t = 8\,\text{s}$ is how many meters per second?
\begin{minipage}{0.45\textwidth} [Figure: $x$(m) vs $t$(s) graph. The curve starts at $x=0$, goes to a minimum near $t=4\,\text{s}$, then rises to $x=12$ and continues increasing in a parabolic (uniform acceleration) shape.] \end{minipage} \begin{minipage}{0.45\textwidth}

• [(1)] $3$
• [(2)] $4$
• [(3)] $6$
• [(4)] $12$

\end{minipage}

The co-ordinates of a moving particle at any time '$t$' are given by $x = \alpha t^{3}$ and $y = \beta t^{3}$. The speed of the particle at time '$t$' is given by
(1) $3t\sqrt{\alpha^{2} + \beta^{2}}$
(2) $3t^{2}\sqrt{\alpha^{2} + \beta^{2}}$
(3) $t^{2}\sqrt{\alpha^{2} + \beta^{2}}$
(4) $\sqrt{\alpha^{2} + \beta^{2}}$

A particle is moving along the $x$-axis with its coordinate with time $t$ given by $x ( t ) = 10 + 8 t - 3 t ^ { 2 }$. Another particle is moving along the $y$-axis with its coordinate as a function of time given by $y ( t ) = 5 - 8 t ^ { 3 }$. At $t = 1 \mathrm {~s}$, the speed of the second particle as measured in the frame of the first particle is given as $\sqrt { v }$. Then $v$ (in $\mathrm { m s } ^ { - 1 }$) is $\_\_\_\_$.

The distance travelled by an object in time $t$ is given by $s = 2.5 t ^ { 2 }$. The instantaneous speed of the object at $t = 5 \mathrm {~s}$ will be :
(1) $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $62.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $12.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$