Question

a car covers a semicircular track of radius 5 m with a constant speed of pie m/s. find the magnitude displacement and average velocity​

Answer 1

Answer:

Displacement = 10m

Average velocity = 2 m/s

Explanation:

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

• A car covers a semicircular track of radius 5 m with a constant speed of π m/s.

We are asked to calculate the magnitude of displacement and average velocity.

★ Calculating displacement :

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Displacement = Shortest\; Distance_{(from \; initial \; \& \; final \; position)} }} }$

Let A to B be the length of semicircular track. We know that the displacement is defined as the shortest distance from the initial and final position. Similarly, A is here initial position and B is final position. The shortest distance will be the straight line from A to B, that is AB. AB is also here diameter of the semi-circle. So,

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

$\\ \longrightarrow \sf{\quad {Displacement = 2 \times r }}$

$\\ \longrightarrow \sf{\quad {Displacement = (2 \times 5) \; m }}$

$\\ \longrightarrow \bf{\quad \underline{Displacement = 10 \; m }}$

Therefore, displacement is 10 m.

★ Calculating average velocity :

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Velocity_{(avg)} = \dfrac{Total \; Displacement}{Total \; Time} }} }$

We need to find total time first.

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Total \; time = \dfrac{Distance}{Speed} }} }$

Since, it is a semicircular track. So, the the distance covered by the car will be the circumference divided by 2.

$\\ \longrightarrow \sf{\quad { Total \; time = \dfrac{\cfrac{2\pi r}{2} }{\pi} }}$

$\\ \longrightarrow \sf{\quad { Total \; time = \cancel{\dfrac{\pi r}{\pi}} }}$

$\\ \longrightarrow \sf{\quad { Total \; time = r }}$

• r = 5 [Given]

$\\ \longrightarrow \bf{\quad \underline{ Total \; time = 5 \; s }}$

Now, we have :

• Total displacement = 10 m
• Total time = 5 s

Substituting values in the formula of average velocity,

$\\ \longrightarrow \sf{\quad { Velocity_{(avg)} = \cancel{\dfrac{10 \; m}{5 \; s} } }}$

$\\ \longrightarrow \bf{\quad \underline{Velocity_{(avg)} = 2 \; m/s }}$

Therefore, average velocity of the car is 2 m/s.