Question

Using the graph calculate the distance travelled​

Answer 1

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Given :- }}}}$

• A graph of motion is given .

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ To Find :- }}}}$

• The distance travelled using the graph .

$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Solution :- }}}}$

The given is a velocity time graph and we know that the area under the ( v - t ) graph gives displacement . Also the slope of the graph , gives the acceleration .

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$\red{\bigstar}\underline{\underline{\textsf{\textbf{ Diagram :- }}}}$

$\setlength{\unitlength}{1 cm}\begin{picture}(12,8)\thicklines\put(0,0){\vector(1,0){7}}\put(0,0){\vector(0,1){5}}\put(0,0.01){\line(1,2){2}}\put(2,4){\line(1,0){2}}\put(4,4){\line(1,-2){2}}\multiput(2,0)(0,1){4}{\line(0,1){0.5}}\multiput(4,0)(0,1){4}{\line(0,1){0.5}}\put(2,-0.7){\sf 20 s}\put(4,-.7){\sf 50 s}\put(-1.6,4){\sf25m/s} \put(6,4){ \boxed{\boxed{\bf @RishabhRanjan}} }\put(1.3,4.2){\sf A}\put(1.5,-0.5){\sf B }\put(0,-0.5){\sf O}\put(4.5,-0.5){\sf C }\put(5.7,-0.5){\sf D}\put(5,4.2){\sf E }\end{picture}$

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➳ Now here , the total distance will be ,

$\sf \dashrightarrow Distance = ar(\triangle AOB ) + ar(\triangle CDE ) + ar( \blacksquare AEBC )\\\\\\\sf\dashrightarrow Distance = \dfrac{1}{2}* 20 * 25 m + 30 * 25 m +\dfrac{ 1}{2}*10 * 25 m\\\\\\\sf\dashrightarrow Distance = 250m + 750m + 125 m \\\\\\\sf\dashrightarrow \underset{\blue{\sf Required\ Distance }}{\underbrace{\boxed{\pink{\frak{ Distance ( s ) = 1125 \ meters }}}}}$ .