Motion in A Straight Line Test - 61

Consider a particle moving along the $$x$$-axis as shown in Fig. 4.138. Its distance from the origin O is described by the coordinate $$x$$ which varies with time. At a time $$t_1,$$ the particle is at point P, where its coordinate is $$x_2$$. The displacement during the time interval from $$t_1$$ and $$t_2$$ is the vector from P to Q the $$x$$-component of this vector is $$(x_2-x_1)$$ and all other component are zero.
 It is convenient to represent the quantity $$x_2-x_1$$, the change in $$x$$, by means of a notation using the Greek letter $$\triangle $$ (capital delta) to designate a change in any quantity. Thus we write $$\triangle x=x_2-x_1$$ in which $$\triangle x$$ is not a product but is to be interpreted as a single symbol representing the change in the quantity $$x$$. Similarly, we denote the time interval from $$t_1$$ to $$t_2$$ as $$t=t_2-t_1.$$
The average velocity of the particle is defined as the ratio of the displacement $$\triangle x$$ to the time interval $$\triangle t$$. We represent average velocity by the letter v with a bar $$\left( \overline { v }  \right) $$ to signify average value. Thus $$\overline { v } =\dfrac { x_{ 2 }-x_{ 1 } }{ t_{ 2 }-t_{ 1 } } =\dfrac { \triangle x }{ \triangle t } $$

A car is moving towards south with a speed of $$20ms^{-1}$$. A motorcyclist is moving towards east with a speed of $$15ms^{-1}.$$ At a certain instant, the motorcyclist is due south of the car and is at a distance of 50 m from the car.