an athlete completes half of the circle of radius 2m in 5 sec. Then the average velocity of the athlete is
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an athlete completes half of the circle of radius 2m in 5 sec. Then the average velocity of the athlete is
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[tex]\color{darkblue}\underline{\underline{\sf Given-}}[/tex]
[tex]\color{darkblue}\underline{\underline{\sf To \:Find-}}[/tex]
➩ Average Velocity
[tex]\color{violet}\bullet\underline{\boxed{\sf V_{av}=\dfrac{Displacement}{Time}}}[/tex]
Displacement is Shortest distance Travelled.
⛬ here Displacement will be = 2R
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 2 × 2
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 4 m
[tex]\implies{\sf v_{av}=\dfrac{4}{5} }[/tex]
[tex]\color{red}\implies{\sf v_{av}=0.8\:m/s}[/tex]
[tex]\color{darkblue}\underline{\underline{\sf Answer-}}[/tex]
Average velocity of athelete is [tex]\color{red}{\sf 0.8m/s}[/tex].
Answer:
The diameter of the circular track is given as 200 m. That is, 2r=200 m.
From this radius is calculated as Radius, r = 100 m.
In 40 sec the athlete complete one round. So, in 2 mins and 20 secs, that is, 140 sec the athlete will complete = 140 / 40 = 3.5 (three and a half) rounds.
One round is considered as the circumference of the circular track.
The distance covered in 140 sec = 2πr×3.5=2×3.14×100×3.5=2200 m.
For each complete round the displacement is zero. Therefore for 3 complete rounds, the displacement will be zero.
At the end of his motion, the athlete will be in the diametrically opposite position. That is, displacement = diameter = 200 m.
Hence, the distance covered is 2200 m and the displacement is 200 m.