Question

Physics Class 9
Chapter 1 : Motion

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Answer 1

From the given, velocity time graph we are asked to find out the displacement.

Explanation: We know that in a velocity time graph the area under the curve tell us about the distance or displacement of the given object or body.

Knowledge required:

• SI unit of velocity is m/s
• SI unit of displacement is m
• SI unit of distance is m
• SI unit of time is s

Where, m is metre, m/s is metre per second and s is second

Required solution:

Explanation: To solve this question we have to find out the area of all the given figures then we have to carry on! Let us find out the area of the given figures individually.

Finding area of rectangle first that is red in colour! (Kindly refer to attachment 1st)

$:\implies \sf Displacement \: = Area \: under \: curve \\ \\ :\implies \sf s \: = Area \: under \: curve \\ \\ :\implies \sf s_1 \: = Area \: of \: rectangle \\ \\ :\implies \sf s_1 \: = Length \times Breadth \\ \\ :\implies \sf s_1 \: = (4-0) \times (2-0) \\ \\ :\implies \sf s_1 \: = 4 \times 2 \\ \\ :\implies \sf s_1 \: = 8 \: m \\ \\ :\implies \sf Area \: = 8 \: m^2$

Finding area of rectangle second that is green in colour! (Kindly refer to attachment 1st)

$:\implies \sf Displacement \: = Area \: under \: curve \\ \\ :\implies \sf s \: = Area \: under \: curve \\ \\ :\implies \sf s_2 \: = Area \: of \: rectangle \\ \\ :\implies \sf s_2 \: = Length \times Breadth \\ \\ :\implies \sf s_2 \: = (6-4) \times (8-0) \\ \\ :\implies \sf s_2 \: = 2 \times 8\\ \\ :\implies \sf s_2 \: = 16 \: m \\ \\ :\implies \sf Area \: = 16 \: m^2$

Finding area of rectangle third that is blue in colour! (Kindly refer to attachment 1st)

Note: This time it doesn't matter that the velocity is in negative axis, find it by using positive sign!

$:\implies \sf Displacement \: = Area \: under \: curve \\ \\ :\implies \sf s \: = Area \: under \: curve \\ \\ :\implies \sf s_3 \: = Area \: of \: rectangle \\ \\ :\implies \sf s_3 \: = Length \times Breadth \\ \\ :\implies \sf s_3 \: = (4-2) \times (+4-0) \\ \\ :\implies \sf s_3 \: = 2 \times +4 \\ \\ :\implies \sf s_3 \: = 8 \: m \\ \\ :\implies \sf Area \: = 8 \: m^2$

Finding area of rectangle fourth that is yellow in colour! (Kindly refer to attachment 1st)

$:\implies \sf Displacement \: = Area \: under \: curve \\ \\ :\implies \sf s \: = Area \: under \: curve \\ \\ :\implies \sf s_4 \: = Area \: of \: rectangle \\ \\ :\implies \sf s_4 \: = Length \times Breadth \\ \\ :\implies \sf s_4 \: = (8-0) \times (8-6) \\ \\ :\implies \sf s_4 \: = 8 \times 2 \\ \\ :\implies \sf s_4 \: = 16 \: m \\ \\ :\implies \sf Area \: = 16 \: m^2$

~ Now let us calculate the displacement!

Explanation: To calculate the displacement in this graph we have to add the area which are in positive axis and have to subtract those are which are in negative axis together

$:\implies \sf Displacement \: = 8 + 16 - 8 + 16 \\ \\ :\implies \sf Displacement \: = 24 + 8 \\ \\ :\implies \sf Displacement \: = 32 \: m$

Therefore, 32 metres is the displacement.

Additional information:

Difference between distance and displacement, (kindly refer to attachment 2nd we getting difficulty to view from app)

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

Learn more:

↪️ The slope of D-T graph gives the _____ of the object in motion.

• The slope of Distance Time or Displacement Time graph give the speed of the object in motion.

↪️ Distance or displacement are same in the matter of graphs in motion

↪️ Speed and Velocity are same in the matter of graphs in motion

↪️ The slope of V-T graph gives the _____ of the object in motion.

• The slope of Velocity Time graph give the acceleration of the object in motion.

↪️ The area under curve of V-T graph gives the _____ of the object in motion.

• The area under curve of Velocity Time graph gives the distance/displacement of the object in motion.