Question

A person moves along the boundary of a square field of side 10m in 40s find the average velocity and average speed of its journey its journey in 3 mins

Answer 1

Hey.

Here is your answer.

Given : Square field of side , a = 10 m

time taken to move along the boundary = 40s

Perimeter of the square field (boundary)

= 4× side

= 4 × 10

= 40 m

So, he travels 40 m in 40 s.

Now as time given : 3 minutes = 3 × 60 s

t = 180 s

Since 40s he takes to travel 40 m

so, in 180 s he will travel a distance of

$= \: \: \frac{40}{40} \times 180$

= 180 m

So, he will travel a total distance of 180m
along the side of the square

so, as the average speed

$= \: \frac{total \: distance}{total \: time}$

so, average speed of the person for 3 minutes

$= \: \frac{180}{180} \: \: \frac{m}{s} \\ \\ \\ = \: \: 1m {s}^{ - 1}$

Now , in 180 m he will take

$\frac{180}{40} \: rounds \: along \: the \: square \\ \\ i.e. \: 4 \: complete \: round \: and \: 20 \: m \: \\ from \: start$

So, it will be diagonally opposite from the start
as the sides are 10+10 m

So, the displacement = diagonal of the square

$\\ dispacement \: = \: side\sqrt{2} \\ \\ = \: \: side \sqrt{2} \: m$

As average velocity

$= \: \frac{displacement}{time} \\ \\ so \: avg \: velocity = \: \frac{10 \times \sqrt{2} }{180} \\ \\ = \: \frac{ \sqrt{2} }{18} \: m {s}^{ - 1}$

Hence, average speed is 1 m/s

whereas average velocity is 0.07856 m/s along the diagonal.

Thanks

Answer 2

Given,

Side of Square = 10 m

Total Distance coverd = Perimeter of Square = 4 x side(a) = 4 x 10 m = 40 m

So, that person takes 40s to transverse 40 m.

=> Speed = Distance/Time

=> Speed = 40/40 m/s

=> Speed = 1 m/s

We have to find Average Speed and Average Velocity in 3 minutes.

=> 3 minutes = (3 x 60)s = 180s

So,

Distance covered in 180 s = Speed x Time = 180 x 1 = 180 m

Now,

=> Average Speed = Total Distance/Total Time

=> Avg(Speed) = 180/180 m/s = 1 m/s

Hence, The Average Speed of person is 1 m/s.

Again,

=> As man moves along Square boundry so that the displacement will be its Diagonal.

$=>Diagonal = Displacement = \sqrt{2} \times a$

$=> Displacement = 10\sqrt{2}$

As we know that,

$=> V_{avg}= Displacement/Total time$

$=> V_{avg} = \frac{10\sqrt{2}}{180}$

$=> V_{avg} = \frac{\sqrt{2}}{180}$

$=> V_{avg} = 0.0785674201$

Hence,

=> Average Speed = 1 m/s

&

=> Average Velocity = 0.0785674201

Be Brainly