Question

An object moves along a circular path of diameter 14 cm with constant speed.If it take 2 minutes to move from a point on the path to the diametrically opposite point. Find distance,speed,displacement,average velocity​

Answer 1

Explanation:

Let us say the body starts moving from Point A. Thus, diametrically opposite point will be Point B.

Calculating distance :

As it is moving on the circular path and we are given that it moves from a point on the path to the diametrically opposite point. Thus, it covered half of the circumference of the circle. So, we can say that,

$\longmapsto \bf { Distance = \dfrac{Circumference}{2} }$

$\longmapsto \rm { Distance = \dfrac{2\pi r}{2} }$

Here, we aren't given the value of radius. We have to calculate it. Since, we know that, diameter is twice the radius. So, radius = diameter ÷ 2, or radius = (14 cm)/2 ; which is 7 cm.

$\longmapsto \rm { Distance = \pi r }$

$\longmapsto \rm { Distance = \Bigg ( \dfrac{22}{7} \times 7 \Bigg ) \; cm }$

$\longmapsto \bf { Distance = 22 \; cm }$

∴ Distance covered is 22 cm.

$\rule{200}2$

Calculating speed :

As we know that,

$\longmapsto \bf { Speed = \dfrac{Distance}{Time} }$

Here, we have calculated distance travelled that is 22 cm.

And, time is 2 minutes.

$\longmapsto \rm { Speed = \dfrac{22\; cm}{2 \; min} }$

$\longmapsto \bf { Speed = 11 \; cm/min }$

∴ Speed of the object is 11 cm/minute.

$\rule{200}2$

Calculating displacement :

Displacement is defined as the shortest distance from initial point to the final point. Shortest distance between two points is always a straight line.

Here, initial point is A and final point is B. The shortest distance from A to B is the diameter of the circle.

$\longmapsto \bf { Displacement = Diameter}$

We are already given in the question that the diameter is 14 cm.

$\longmapsto \bf { Displacement = 14 \; cm}$

∴ Displacement is 14 cm.

$\rule{200}2$

Calculating average velocity :

Formula of average velocity is :

$\longmapsto \bf { Velocity_{(avg)} = \dfrac{Total \; displacement}{Total \; time} }$

• Total displacement = 14 cm
• Total time = 2 minutes

$\longmapsto \rm { Velocity_{(avg)} = \dfrac{14 \; cm}{2 \; min} }$

$\longmapsto \bf { Velocity_{(avg)} = 7 \; cm/min }$

∴ Average velocity is 7 cm/min.

$\rule{200}2$