Question

How far does the runner whose velocity–time graph is shown in the figure travel in 16 s? The figure's vertical scaling is set by vs = 8.00 m/s.

2 4 0 (s/u)

Answer 1

v-velocity , s-distance, t-time

v=ds/dt

ds=vdt

$s=\int vdt$

Integration is area under the curve, therefore to calculate the distance covered using above velocity profile

can be calcualted by calculating total area covered velocity curve over time. Refer the figure given below to calculate the total area.

$area of triangle=\frac{1}{2}\times height\times length$

$area of rectangle= length\times breadth$

$s=\frac{1}{2} \times 2\times 8+8 \times 8+\frac{1}{2}\times 4\times 2+4\times 4$

$s=100m$