Question

A cyclist is moving on circular track of diameter 70 m, calculate distance and displacement after 4.5 rounds.

1. 770 m, 35 m
2. 990 m, 70m
3. 880 m, 70m
4. 440 m, 70 m

Answer 1

Answer:

2. 990 m, 70m

Explanation:

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

• A cyclist is moving on circular track of diameter 70 m. (So, Radius = 35 m)

We've been asked to calculate distance travelled and displacement.

In order to calculate the distance travelled, firstly we need to find the distance travelled in 1 round. Distance travelled in one round will be given by the circumference of the circular track. Let the distance travelled be S.

• $\boxed{ \sf\purple{ C = 2\pi r }}$

$\longrightarrow \sf{\quad { S = Circumference }}$

$\longrightarrow \sf{\quad { S = (2 \pi r) \times 4.5 }}$

$\longrightarrow \sf{\quad { S = \Bigg \lgroup 2 \times \dfrac{22}{7} \times 35 \times 4.5 \Bigg \rgroup \; m }}$

$\longrightarrow \sf{\quad { S = \Bigg \lgroup 2 \times 22 \times 5 \times 4.5 \Bigg \rgroup \; m }}$

$\longrightarrow \quad { \underline{\boxed{ \textbf{\textsf{S = 990 \; m}} }}} \; \purple{\bigstar}$

∴ Distance travelled is 990 m.

Now, we have to find the displacement. Here, the body's initial position is A and the final position is B. After covering 4 rounds, it'll come to point A. Then, he'll cover 0.5 rounds in order to complete 4.5 rounds. And, at last it's come to point B. This, as the displacement is the shortest distance from initial position to final position, so the displacement is AB.

$\longrightarrow \sf{\quad { Displacement = Diameter }}$

$\longrightarrow \quad { \underline{\boxed{ \textbf{\textsf{Displacement = 70 \; m}} }}} \; \purple{\bigstar}$

∴ Displacement is 70 m.

$\longrightarrow \large\underline{ \boxed {\textbf{\textsf{\purple{Option \; 2}}} !!}}$