Question

A body travels along a circular path of radius 70 m. After travelling half a revolution in 20 s, find the (i) average velocity,(ii) average speed.

Answer 1

Gɪᴠᴇɴ :-

• Radius(r)= 70m
• Time taken (t) = 20s
• Path travelled = Half of circle

Tᴏ ғɪɴᴅ :-

• Average velocity
• Average speed

sᴏʟᴜᴛɪᴏɴ :-

Now,

• Displacement = Diameter of circle

• Diameter = 2r = 2×70 = 140 m

$\implies \sf \: Average \: Velocity \: = \frac{Displacement}{Time} \\ \\ \\ \implies \sf \: \frac{140}{20} \\ \\ \\ \implies \sf \: 7m {s}^{ - 1}$

• Average velocity = 7 m/s

Now ,

• Distance covered by body = Circumference of Semi - circle

• Circumference of semi circle = πr

We get,

↣ Distance = πr = 22/7 × 70

↣ 22 × 10

↣ 220 m

Now,

$\implies\sf Average\:Speed\: = \dfrac{Total \: Distance \: Travelled}{Total \: Time \: Taken} \\ \\ \\ \implies\sf \: \dfrac{220}{20} \\ \\ \\ \implies\sf \: 11m {s}^{ - 1}$

• Average speed = 11 m/s

Answer 2

Given :-

→ A body travels along a circular path of radius 70 m. It travels half a revolution is 20 s.

• Radius of the path, r = 70 m
• Time taken, t = 20 s

$\underline{\rule{170}2}$

To find :-

The (i) average velocity, and the

(ii) average speed.

$\underline{\rule{170}2}$

We must know :-

$\boxed{\bigstar\ \sf{\color{red}{Average\ speed=\dfrac{Total\ distance\ covered}{Total\ time\ taken} }}}$

And

$\boxed{\bigstar\ \sf{\color{red}{Average\ velocity=\dfrac{Total\ displacement}{Total\ time\ taken} }}}$

$\underline{\rule{170}2}$

Solution :-

◙ Distance travelled by the body(s) = 1/2 × Perimeter of the path

(As distance is the total length of the path covered between the initial point and the final position).

⇒s = 1/2 × 2πr

⇒s = πr

Taking π as 22/7,

⇒s = 22/7 × 70

⇒s = 22 × 10

⇒s = 220 m

$\rule{100}2$

Overall displacement of the body(x) = Diameter of the path

(As displacement is the shortest path covered between the initial point and the final position).

⇒x = 2r

⇒x = 2 × 70

⇒x = 140 m

$\rule{100}2$

(i) Now,

• s = 220 m
• t = 20 s

Average speed = s/t

⇒Average speed = 220/20

⇒Average speed = 11 m/s

$\rule{100}2$

(ii) Again,

• x = 140 m
• t = 20 s

Average velocity = x/t

⇒Average velocity = 140/20

⇒Average velocity = 7 m/s