Question

If a trolley starts from rest with an acceleration of 2 cm/s2 ,find the velocity of the body after 3 s.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Velocity\:after\:3\:sec=6\:cm/s^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given: }} \\ \tt: \implies Acceleration(a) = 2 \: {cm/s}^{2} \\ \\ \tt: \implies Time(t) = 3 \: sec \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies Final \: velocity(v) =?$

• According to given question :

$\tt \circ \: Initial \: velocity = 0 \: m/s \\ \\ \bold{As \: we \: know \: that } \\ \tt: \implies v = u + at \\ \\ \tt: \implies v = 0 + 2 \times 3 \\ \\ \tt: \implies v = 2 \times 3 \\ \\ \green{\tt: \implies v = 6 \: {cm/s}^{2} } \\ \\ \green{\tt \therefore Velocity \: after \: 3 \: sec \: is \: 6 \: {cm/s}^{2} }\\\\ \blue{\bold{Some \: related \: formula}} \\ \orange{\tt \circ \: {v}^{2} = {u}^{2} + 2as} \\ \\ \orange{\tt \circ \: s = ut + \frac{1}{2} {at}^{2} }$

Answer 2

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✺Answer:

♦️GiveN:

• Trolley was initially at rest.
• Started with accleration 2 cm/s^2
• Time travelled = 3 seconds.

♦️To FinD:

• Velocity after 3 s.

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✺Explanation Of Concept:

The above question is very simple and based on equations of motion. After knowing all the equations of motion (Kinematics equations), which can find the solution as it is an "Apply Formula and get solution" type question.

✍Three Equations of Motion:

$\large{ \circ \: \: { \rm{ \red{v = u + at}}..........(1)}} \\ \large{ \circ \: \: { \rm{ \red{ {v}^{2} - {u}^{2} = 2as}}..........(2)}} \\ \large{ \circ \: \: { \rm{ \red{s = ut + \frac{1}{2} a {t}^{2} }}...........(3)}}$

✒Note:

Symbols have their Usual Meanings

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By using these formulas, we can solve the question and we have our required other quantities.

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✺Solution:

• Initial velocity = 0 m/s
• Accleration = 2 cm/s^2
• Time taken = 3 seconds

Let the final velocity be v.

By using 1st equation of motion ,

$\large{ \rm{ \rightarrowtail \: v = u + at}} \\ \\ \large{ \rm{ \rightarrowtail \: v = 0 + 2 \: cm {s}^{ - 2} \times 3 \: s}} \\ \\ \large{ \rm{ \rightarrowtail \: v = \boxed{ \blue{ \rm{6 \: cm {s}^{ - 1} }}}}} \\ \\ \large{ \therefore{ \underline{ \green{ \rm{ \: final \: velocity \tiny{(in \: cm {s}^{ - 1} )} \large{ = 6 \: cm {s}^{ - 1} }}}}}}$

• We know that 1 cm = 0.01 m
• So, we can say that 1 cm/s = 0.01 m/s

$\large{ \rm{ \rightarrowtail \: v \tiny{(m {s}^{ - 1})} \large{= 6 \times 0.01 = \boxed{ \rm{ \blue{ 0.06 \: m {s}^{ - 1}}}}}}} \\ \\ \large{ \therefore{ \underline{ \green{ \rm{final \: velocity \tiny{(in \: m {s}^{ - 1})} \large {= 0.06 \: m {s}^{ - 1} }}}}}}$

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