A circular cycle track has a circumference of $314\, m$ with $A B$ as one of its diameter. $A$ cyclist travels from $A$ to $B$ along the circular path with a velocity of constant magnitude $15.7\, m s ^{-1}$. Find the
$(a)$ distance moved by the cyclist.
$(b)$ displacement of the cyclist, if $A B$ represents north$-$south direction.
$(c)$ the average velocity of the cyclist.
A circular cycle track has a circumference of $314\, m$ with $A B$ as one of its diameter. $A$ cyclist travels from $A$ to $B$ along the circular path with a velocity of constant magnitude $15.7\, m s ^{-1}$. Find the
$(a)$ distance moved by the cyclist.
$(b)$ displacement of the cyclist, if $A B$ represents north$-$south direction.
$(c)$ the average velocity of the cyclist.
$(a)$ Distance travelled by the cyclist $=$ length of the path $AB$ $=$ half the circumference of the circle
$S=\frac{314}{2}=157 m$
$(b)$ The displacement of the cyclist is equal to the diameter $AB$ of the circle.
Now, circumference $=2 \pi r=314,$ therefore,
$r=\frac{\text { circumference }}{2 \pi}=\frac{314}{2 \times 3.14}=50 m$
Therefore, displacement of the cyclist $=2 \times$ $50=100 \,m$ towards south.
$(c)$ Since the magnitude of velocity is constant, therefore, the average velocity is equal to the velocity with which the cyclist moves. Therefore, average velocity $=15.7 m s ^{-1}$
Similar Questions
$(a)$ Differentiate acceleration from velocity.
$(b)$ Can a body have acceleration without change in magnitude of velocity ? Explain with an example.
$(c)$ A motor boat starting from rest on a lake accelerates in a straight line at a constant rate of $3\, m s ^{-2}$ for $8 \,s$. How far does the boat travel during this time ?
$(a)$ Differentiate acceleration from velocity.
$(b)$ Can a body have acceleration without change in magnitude of velocity ? Explain with an example.
$(c)$ A motor boat starting from rest on a lake accelerates in a straight line at a constant rate of $3\, m s ^{-2}$ for $8 \,s$. How far does the boat travel during this time ?
Using following data, draw time-displacement graph for a moving object :
Time $(s)$
$0$
$2$
$4$
$6$
$8$
$10$
$12$
$14$
$16$
Displacement $(m)$
$0$
$2$
$4$
$4$
$4$
$6$
$4$
$2$
$0$
Use this graph to find average velocity for first $4\,\sec $, for next $4\,\sec $ and for last $6\,\sec $.
Using following data, draw time-displacement graph for a moving object :
| Time $(s)$ | $0$ | $2$ | $4$ | $6$ | $8$ | $10$ | $12$ | $14$ | $16$ |
| Displacement $(m)$ | $0$ | $2$ | $4$ | $4$ | $4$ | $6$ | $4$ | $2$ | $0$ |
Use this graph to find average velocity for first $4\,\sec $, for next $4\,\sec $ and for last $6\,\sec $.
What is meant by free fall ? Two bodies, one of mass $1\,g$ and other of mass $1\, kg$ are dropped from the same height in vacuum. Compare the two time intervals in which the two bodies will hit the ground.
What is meant by free fall ? Two bodies, one of mass $1\,g$ and other of mass $1\, kg$ are dropped from the same height in vacuum. Compare the two time intervals in which the two bodies will hit the ground.
Answer the following questions
$(i)$ State the type of motion shown by a freely falling stone.
$(ii)$ When a stone is thrown vertically upwards its velocity is continuously decreased. Why ?
$(iii)$ Give an example of a motion in which average velocity is zero, but the average speed is not zero.
Answer the following questions
$(i)$ State the type of motion shown by a freely falling stone.
$(ii)$ When a stone is thrown vertically upwards its velocity is continuously decreased. Why ?
$(iii)$ Give an example of a motion in which average velocity is zero, but the average speed is not zero.
If the displacement of an object is proportional to square of time, then the object moves with
If the displacement of an object is proportional to square of time, then the object moves with