Question

an object starting from rest accelerates in a straight line at a constant rate of 5 m/s2 for 10s. calculate the magnitude of displacement during this time

Answer 1

Answer:

Provided that:

• Initial velocity = 0 m/s
• Acceleration = 5 m/s sq.
• Time = 10 seconds

To calculate:

• The displacement

Solution:

• The displacement = 250 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:

$:\implies \sf s \: = ut \: + \dfrac{1}{2} \: at^2 \\ \\ :\implies \sf s \: = 0(10) + \dfrac{1}{2} \times 5(10)^{2} \\ \\ :\implies \sf s \: = 0(10) + \dfrac{1}{2} \times 5(100) \\ \\ :\implies \sf s \: = 0(10) + \dfrac{1}{2} \times 500 \\ \\ :\implies \sf s \: = 0 + \dfrac{1}{2} \times 500 \\ \\ :\implies \sf s \: = \dfrac{1}{2} \times 500 \\ \\ :\implies \sf s \: = 250 \: m \\ \\ :\implies \sf Displacement \: = 250 \: metres$

Therefore, 250 m is displacement!

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=0m/s
• Acceleration=a=5m/s^2
• Time=t=10s
• Displacement=s

We know

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

$\\ \sf \longmapsto s=0(10)+\dfrac{1}{2}5(10)^2$

$\\ \sf \longmapsto s=\dfrac{5\times 100}{2}$

$\\ \sf \longmapsto s=\dfrac{500}{2}$

$\\ \sf \longmapsto s=250m$