Question

A cart rolling down an incline for 5.0 seconds has an acceleration of 4.0 m/s/s. If the cart has a beginning speed of 2.0 m/s, what is its final speed (in m/s)?

Answer 1

$\sf Given \begin{cases} & \sf{Initial\;speed,\;u = 2.0\;m/s } \\ & \sf{Acceleration,\;a = 4.0\;m/s^2} \\ & \sf{Time,\;t = 5.0\;s} \end{cases}$

We have to find final Velocity, v?

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Using First equation of motion,

$\star\;{\boxed{\sf{\purple{v = u + at}}}}$

$:\implies\sf v = 2.0 + 4.0 \times 5$

$:\implies\sf v = 2.0 + 20.0$

$:\implies{\boxed{\frak{\pink{v = 22.0\;m/s}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\; Final\; velocity\;of\;cart\;is\;\bf{22.0\;m/s.}}}}$

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$\qquad\qquad\boxed{\underline{\underline{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}$

★ There are three equations of motion:-

⠀⠀⠀✩ $\sf v = u + at$

⠀⠀⠀✩ $\sf s = ut + \dfrac{1}{2} at^2$

⠀⠀⠀✩ $\sf v^2 - u^2 = 2as$

⠀⠀ ━━━━━━━━━━━━━━━━━━━━━

$\;\;\star\;\sf Acceleration (a) = \dfrac{Final\; velocity (v) - Initial\; velocity (u)}{Time (t)}$

Answer 2

Explanation:

Initialspeed,u=2.0m/s

Acceleration,a=4.0m/s

2

Time,t=5.0s

We have to find final Velocity, v?

━━━━━━━━━━━━━━━━━━━━━━━━━

Using First equation of motion,

\begin{gathered}\star\;{\boxed{\sf{\purple{v = u + at}}}}\\ \\\end{gathered}

⋆

v=u+at

\begin{gathered}:\implies\sf v = 2.0 + 4.0 \times 5\\ \\\end{gathered}

:⟹v=2.0+4.0×5

\begin{gathered}:\implies\sf v = 2.0 + 20.0\\ \\\end{gathered}

:⟹v=2.0+20.0

\begin{gathered}:\implies{\boxed{\frak{\pink{v = 22.0\;m/s}}}}\;\bigstar\\ \\\end{gathered}

:⟹

v=22.0m/s

★

\therefore\;{\underline{\sf{Hence,\; Final\; velocity\;of\;cart\;is\;\bf{22.0\;m/s.}}}}∴

Hence,Finalvelocityofcartis22.0m/s.

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\begin{gathered}\qquad\qquad\boxed{\underline{\underline{\bigstar \: \bf\:More\:to\:know\:\bigstar}}} \\ \\\end{gathered}

★Moretoknow★

★ There are three equations of motion:- \begin{gathered}\\ \\\end{gathered}

⠀⠀⠀✩ \sf v = u + atv=u+at

⠀⠀⠀✩ \sf s = ut + \dfrac{1}{2} at^2s=ut+

2

1

at

2

⠀⠀⠀✩ \sf v^2 - u^2 = 2asv

2

−u

2

=2as

⠀⠀ ━━━━━━━━━━━━━━━━━━━━━

\;\;\star\;\sf Acceleration (a) = \dfrac{Final\; velocity (v) - Initial\; velocity (u)}{Time (t)}⋆Acceleration(a)=

Time(t)

Finalvelocity(v)−Initialvelocity(u)