Question

(a) Find the average speed of a bicycle if it completes two round of a circular track of radius

140 m twice in 5 min 52 sec.

(i) 10 m/s (ii) 5 m/s (iii) 2 m/s (iv) 4 m/s​

Answer 1

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✺Answer:

♦️GiveN:

• Travelled in a circular path and completed two revolutions.
• Radius of the path = 140 m
• Time taken = 5 min 52 sec

♦️To FinD:

• Speed of the Bicycle...?

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✺Explanation of Q.

The question is asking to find the average speed when distance travelled and time taken are given. Before that, In short we should have a rough idea about Average speed.

So, What is Avg. Speed?

✍ The average speed of a body is the total distance travelled by total time taken. In case, of uniform motion, Average speed = Instataneous speed.

$\large{ \ast{ \boxed{ \purple{ \rm{ \: Avg. \: speed = \frac{total \: distance \: travelled}{total \: time \: taken} }}}}}$

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Thus, for solving this question we need to find the total distance travelled by the bicycle by total time taken.

▶️ Refer to the attachment....

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✺Solution:

The bicyclist covered a distance = 2 × ( Perimeter/ circumference of the circular path)

Finding the total distance

$\large{ \rm{ \ast \: Circumference \: of \: circle = 2\pi \: r}} \\ \\ \large{ \rm{ \rightarrow \: Distance = \: 2 \times circumference}} \\ \\\large{ \rm{ \rightarrow \: Distance = 2 \times 2\pi \: r}} \\ \\ \large{ \rm{ \rightarrow \: Distance = 4\pi \times \: 140 \: m}} \\ \\ \large{ \rm{ \rightarrow \: Distance = 4 \times \frac{22}{7} \times 140 \: m}} \\ \\ \large{ \rm{ \rightarrow \: Distance = 4 \times 22 \times \cancel{\frac{140}{7} \: m}}} \\ \\ \large{ \rm{ \rightarrow \: Distance = 4 \times 22 \times 20 \: m}} \\ \\ \large{ \rm{ \rightarrow \: Distance = \boxed{ \red{1760 \: m}}}}$

So, total distance = 1760 m

And, Time taken = 5 min 52 sec

Converting into seconds,

$\large{ \rm{ \ast \:1 \:min = 60 \: sec}} \\ \\ \large{ \rm{ \rightarrow \: Total \: time \: taken = 5 \: min \: 52 \: sec}} \\ \\ \large{ \rm{ \rightarrow \: Total \: time \: taken = 5 \times 60 + 52 \: sec}} \\ \\ \large{ \rm{ \rightarrow \: Total \: time \: taken = \boxed{ \red{352 \: sec}}}}$

Now, we have got our total distance and total time, now we can use the formula to solve the question.

By using Formula,

$\large{ \rm{ \ast \: Avg. \: speed = \frac{total \: distance}{total \: time}}} \\ \\ \large{ \rm{ \rightarrow \: Avg. \: speed = \frac{1760 \: m}{352 \: s} }} \\ \\ \large{ \rm{ \rightarrow \: Avg. \: speed = \boxed{ \red{5 \: m {s}^{ - 1} }}}}$

✒Average speed of Bicycle = 5 m/s

$\large{ \rm{ \ast \underline{ \pink{\: Option \: ( ii)\: }}}}$

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