Question

Acceleration of a particle starting from rest a=6t then find velocity at t=1sec

Answer 1

Correct Question: Acceleration of a particle starting from rest is 6 m/s sq. then find velocity at time 1 second.

Provided that:

• Acceleration = 6 m/s sq.
• Initial velocity = 0 m/s
• Time taken = 1 second

To calculate:

• The final velocity

Solution:

• The final velocity = 6 m/s

Using concept:

• Acceleration formula

Or

• First equation of motion

Using formula:

• ${\small{\underline{\boxed{\sf{a \: = \dfrac{v-u}{t}}}}}}$

Or first equation of motion is given by

• ${\small{\underline{\boxed{\sf{v \: = u \: + at}}}}}$

[Where, a denotes acceleration, v denotes final velocity, u denotes initial velocity, t denotes time taken]

Required solution:

~ 1st method by using acceleration formula!

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time \: taken} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf 6 = \dfrac{v-0}{1} \\ \\ :\implies \sf 6 = \dfrac{v}{1} \\ \\ :\implies \sf 6 \times 1 \: = v \\ \\ :\implies \sf 6 \: = v \\ \\ :\implies \sf v \: = 6 \: ms^{-1} \\ \\ :\implies \sf Final \: velocity \: = 6 \: ms^{-1}$

~ 2nd method by using first equation of motion!

$:\implies \sf v \: = u \: + at \\ \\ :\implies \sf v \: = 0 + (6)(1) \\ \\ :\implies \sf v \: = 0 + 6 \\ \\ :\implies \sf v \: = 6 \: ms^{-1} \\ \\ :\implies \sf Final \: velocity \: = 6 \: ms^{-1}$

Additional information:

$\begin{gathered}\boxed{\begin{array}{c|cc}\bf Speed&\bf Velocity\\\frac{\qquad \qquad \qquad\qquad\qquad \qquad\qquad\qquad}{}&\frac{\qquad \qquad \qquad\qquad\qquad \qquad\qquad\qquad}{}\\\sf The \: distance \: travelled \: by &\sf The \: distance \: travelled \: by \\ \sf \: a \: body \: per \: unit \: time&\sf \: a \: body \: per \: unit \: time \\ &\sf in \: a \: given \: direction \\\\\sf It \: is \: scalar \: quantity. &\sf It \: is \: vector \: quantity \\\\\sf It \: is \: positive \: always &\sf It \: can \: be \: \pm \: \& \: 0 \: too \\\\\sf Speed \: = \dfrac{Distance}{Time} &\sf Velocity \: = \dfrac{Displacement}{Time} \end{array}}\end{gathered}$

Answer 2

Answer:-

• Acceleration=6m/s$^2$=a
• Initial velocity=u=0m/s
• Time=t=1s
• Final velocity=v=?

We know that

$\boxed{\sf v=u+at}$

$\\ \qquad\quad\sf{:}\longrightarrow v=0+6(1)$

$\\ \qquad\quad\sf{:}\longrightarrow v=0+6$

$\\ \qquad\quad\sf{:}\longrightarrow v=6m/s$