Question

The graph below represents the motion of a remote control car back and forth along a straight line path.
What is the average velocity of the car during the first $25$ seconds of its motion?

• A. $8.0m/s$
• B. $7.0m/s$
• C. $5.0m/s$
• D. $4.0m/s$
• E. $3.0m/s$

Answer 1

The correct option is E $3.0m/s$

The displacement in a velocity-time graph is given by the area under velocity graph and time axis .

positive displacement from 0 to 17.5 s $=$area of triangle upto 5 s +area of square upto 15s+area of triangle upto 17.5 s ,

or positive displacement $=1/2\times 5\times 10+10\times 10+1/2\times 2.5\times 10=137.5m$

negative displacement from 17.5 to 25 s $=$area of triangle upto 20 s +area of rectangle upto 25s

or negative displacement $=-(1/2\times 2.5\times 10+10\times 5)=-62.5m$

therefore total displacement $=137.5-62.5=75m$

now average velocity =total displacement /total time ,

$v_{av}=75/25=3m/s$