Question

The time taken by the object for completing 7 rounds along the circular path of radius 3.5 m
with a constant speed of 11 m/s is:

Answer 1

Answer:

In one complete cycle, it comes back to its initial position, so the displacement of the object is zero.

Distance travelled = circumference of the circle = 2πr

                                                                               =2×  

7

22

​

×3.5

                                                                               =22m

Answer 2

$\Large {\underline {\purple{ \bf { Solution :}}}}$

As per the provided information in the given question, we have :

• Speed of the object = 11 m/s
• Radius of the circular path = 3.5 m

We've been asked to calculate the time taken to complete 7 rounds of the circular path.

Here, in order to calculate the the time taken to complete 7 rounds of the circular path, firstly we need find the distance covered by the object in 1 round. Distance covered by the object in 1 round will be the circumference of the circular path.

$\implies \sf {Distance_{(1 \; round)} = Circumference }$

$\implies \sf {Distance_{(1 \; round)} = 2\pi r }$

$\implies \sf {Distance_{(1 \; round)} = 2 \times \dfrac{22}{7} \times 3.5 \; m }$

$\implies \sf {Distance_{(1 \; round)} = 2 \times \dfrac{22}{\cancel{7}} \times \dfrac{\cancel{35}}{10} \; m }$

$\implies \sf {Distance_{(1 \; round)} = 2 \times 22 \times \dfrac{5}{10} \; m }$

$\implies \sf {Distance_{(1 \; round)} = 2 \times 22 \times \dfrac{1}{2} \; m }$

$\implies \boxed{ \sf {Distance_{(1 \; round)} = 22 \; m} }$

Now, distance covered in 1 round is 22 m. So,

$\implies \sf {Distance_{(7 \; rounds)} = 7 \times 22 \; m }$

$\implies \boxed{\purple{ \sf {Distance_{(7 \; rounds)} = 154 \; m}} }$

$\rule{200}{2}$

Now, we have :

• Distance covered in 7 rounds = 154 m
• Speed (Constant) = 11 m/s

We know that,

$\bigstar \;\; \underline {\boxed { \pmb{\sf{\pink{ Time}}} = \dfrac{ \pmb{\sf{\pink{ Distance}}}}{ \pmb{\sf{\pink{Speed}}}} }}$

So,

$\implies \sf {Time = \dfrac{154}{11} \; s }$

$\implies\underline{ \boxed{\purple{ \sf {Time= 14 \; s}} }}$

Therefore, the taken by the object for completing 7 rounds along the circular path is 14 seconds.

$\rule{200}{2}$