Question

an athlete completes 5 rounds of a circular track of diameter 10 metre in 15 minutes. calculate velocity and speed of the athlete​

Answer 1

Given

• Number of rounds = 5
• Diameter = 10 m
• Time = 15 min

To Find

• Velocity & Speed of the athlete

Solution

☯ Velocity = Displacement/Time

• Where displacement is the shortest distance between the starting & ending point

☯ Speed = Distance/Time

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✭ Velocity of the athlete :

➞ Velocity = Displacement/Time

• Displacement = 0 m (as the initial & the final points are the same after 5 rounds)
• Time = 15 min = 15 × 60 = 900 sec

➞ Velocity = 0/900

➞ Velocity = 0 m/s

━━━━━━━━━━━━━━━━━━━━━━━━━

✭ Speed of the athlete :

➞ Speed = Distance/Time

• Distance = Circumference = 2πr = {2 × 22/7 × 5}×5 = 157m
• Time = 900 sec

➞ Speed = 157/900

➞ Speed = 0.174 m/s

∴ The velocity of the athlete us 0 m/s & his speed is 0.174 m/s

Answer 2

$\huge \fbox{ANSWER}$

$\large \underline{ \underline{ \frak{ \color{red}Given:}}}$

$\mapsto \sf{Numbers \: of \: rounds=5 rounds}$

${ \mapsto \sf{Diameter \: of \: circular \: track = 10m}}$

$\mapsto \sf{Time=15min}$

$\large \underline{ \underline{ \frak{ \color{cyan}To \: find:}}}$

$\leadsto \sf{Velocity \: and \: Speed \: of \: athlete. }$

$\large \underline{ \underline{ \frak{ \color{peru}Formula \: used:}}}$

$\dag{ \boxed {\rm{Velocity(v)= \frac{Displacement (S)}{Time(t)} }}}$

$\dag{ \boxed{ \rm{Speed= \frac{Distance }{Time} }}}$

$\large \underline{ \underline{ \frak{ \color{blue}ᴀccording \: to \: Question:}}}$

${ \dashrightarrow{\sf{Velocity(v)= \frac{Displacement (S)}{Time(t)} }}}$

${ \dashrightarrow{\sf{Velocity(v)= \frac{0}{15 \times 60}m {s}^{ - 1} }}}$

${ \dashrightarrow{\sf{Velocity(v)= \frac{0}{900}m {s}^{ - 1} }}}$

${ \dashrightarrow{\sf{Velocity(v)= 0m {s}^{ - 1} }}}$

$\bf \underline{ᴛʜᴇɴ,}$

${ \dashrightarrow{ \sf{Speed= \frac{Distance }{Time} }}}$

${ \dashrightarrow{ \sf{Speed= \frac{2\pi r \times 5round }{900} m {s}^{ - 1} }}}$

${ \dashrightarrow{ \sf{Speed= \frac{2 \times \frac{22}{7} \times \frac{10}{2} \times 5}{900} m {s}^{ - 1} }}}$

${ \dashrightarrow{ \sf{Speed= \frac{157}{900}m {s}^{ - 1} }}}$

${ \dashrightarrow{ \sf{Speed= 0.174m {s}^{ - 1} }}}$

$\bf \underline{ʜᴇɴᴄᴇ,}$

$\: \: \: \: \: \star{ \boxed {\rm{Velocity(v)= 0m {s}^{ - 1} }}}$

$\: \: \: \: \: \star{ \boxed {\rm{Speed= 0.174m {s}^{ - 1} }}}$

$\bf \underline{ɴᴏᴛᴇ:}$

$\sf{Here,athlete \: complete \: his \: 5rounds \: on }$

$\sf{the \: circular \: track \: so \: the \: displacement \: is }$

$\sf{0m/s. }$