The velocity-time graph of a body moving in a | vedclass

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(C) Displacement is the area under the velocity-time graph considering the sign of velocity. Distance is the area under the velocity-time graph taking

Vedclass · Accepted Answer

$5: 9$

Vedclass · Answer

(C) Displacement is the area under the velocity-time graph considering the sign of velocity. Distance is the area under the velocity-time graph taking the absolute value of velocity.For $t = 0$ to $2 \ s$: Velocity $v = 3 \ m/s$. Area $= 3 	imes 2 = 6 \ m$.For $t = 2$ to $3 \ s$: Velocity $v = -2 \ m/s$. Area $= -2 	imes 1 = -2 \ m$.For $t = 3$ to $5 \ s$: Velocity $v = 2 \ m/s$. Area $= 2 	imes 2 = 4 \ m$.For $t = 5$ to $6 \ s$: Velocity $v = -2 \ m/s$. Area $= -2 	imes 1 = -2 \ m$.For $t = 6$ to $8 \ s$: Velocity $v = 2 \ m/s$. Area $= 2 	imes 2 = 4 \ m$.Total Displacement $= 6 - 2 + 4 - 2 + 4 = 10 \ m$.Total Distance $= |6| + |-2| + |4| + |-2| + |4| = 6 + 2 + 4 + 2 + 4 = 18 \ m$.Ratio of displacement to distance $= 10 / 18 = 5 / 9$.

The velocity-time graph of a body moving in a straight line is shown in the figure. The ratio of displacement to distance travelled by the body in time $t = 0$ to $t = 8 \ s$ is:

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