Chapter 3, Problem 8STP

To determine

To Choose: The correct option.

Answer to Problem 8STP

Option B: $125\text{m}$ North

Explanation of Solution

Given:

A velocity-time graph.

  

Formula Used:

Displacement can be calculated from the velocity-time graph by measuring the area under the curve.

Area of trapezium can be obtained by:

  $A=\frac{1}{2}\left(a+b\right)\times h$

Where, a and b are length of the parallel sides and h is the perpendicular distance between them.

Calculations:

Area of trapezium ABCD:

  $\begin{array}{c}{A}_1=\frac{1}{2}\left(AD+BC\right)\left(AB\right)\\ =\frac{1}{2}\left(20+25\right)\left(25\right)\\ =562.5\text{m}\end{array}$

Area of trapezium CEFG:

  $\begin{array}{c}{A}_2=\frac{1}{2}\left(CG+EF\right)\left(GF\right)\\ =\frac{1}{2}\left(20+15\right)\left(-25\right)\\ =-437.5\text{m}\end{array}$

Net displacement:

  $\begin{array}{l}{A}_1+A_2\\ =562.5-437.5\\ =125\text{m}\left(\text{north}\right)\end{array}$

Conclusion:

Thus, correct option is B.