Question

A particle moving with an initial velocity of 5m/s is subjected to a uniform acceleration of 2 m/s2. Find the displacement in the next 4 sec.?

answer fast with explanation​

Answer 1

Answer:

Provided that:

• Initial velocity = 5 m/s
• Acceleration = 2 m/s²
• Time = 4 seconds

To calculate:

• The displacement

Solution:

• The displacement = 36 m

Using concept:

• Second equation of motion

Using formula:

${\small{\underline{\boxed{\sf{\rightarrow s \: = ut \: + \dfrac{1}{2} \: at^2}}}}}$

Where, s denotes displacement or distance or height, u denotes initial velocity, t denotes time taken and a denotes acceleration.

Required solution:

$:\implies \sf s \: = ut \: + \dfrac{1}{2} \: at^2 \\ \\ :\implies \sf s \: = 5(4) + \dfrac{1}{2} \times 2(4)^{2} \\ \\ :\implies \sf s \: = 20 + \dfrac{1}{2} \times 2(16) \\ \\ :\implies \sf s \: = 20 + \dfrac{1}{2} \times 32 \\ \\ :\implies \sf s \: = 20 + 1 \times 16 \\ \\ :\implies \sf s \: = 20 + 16 \\ \\ :\implies \sf s \: = 36 \: m \\ \\ :\implies \sf Displacement \: = 36 \: metres$

Henceforth, the displacement is 36 metres in next 4 seconds!

Knowledge booster:

$\begin{gathered}\boxed{\begin{array}{c|cc}\bf Distance&\bf Displacement\\\frac{\qquad \qquad \qquad\qquad\qquad \qquad\qquad\qquad}{}&\frac{\qquad \qquad \qquad\qquad\qquad \qquad\qquad\qquad}{}\\\sf Path \: of \: length \: from \: which &\sf The \: shortest \: distance \: between \\ \sf \: object \: is \: travelling \: called \: distance. &\sf \: the \: initial \: point \: \& \: final \\ &\sf point \: is \: called \: displacement. \\\\\sf It \: is \: scalar \: quantity. &\sf It \: is \: vector \: quantity \\\\\sf It \: is \: positive \: always &\sf It \: can \: be \: \pm \: \& \: 0 \: too \end{array}}\end{gathered}$

Answer 2

Answer:-

• initial velocity=u=5m/s
• Acceleration=a=2m/s^2
• Time=t=4s
• Displacement=s=?

According to second equation of kinematics

$\boxed{\sf s=ut+\dfrac{1}{2}at^2}$

$\\ \sf \longmapsto s=5(4)+\dfrac{1}{2}2(4)^2$

$\\ \sf \longmapsto s=20+16$

$\\ \sf \longmapsto s=36m$