Question

A car covers a semi circular track of radius 5 m at a speed of pi m/s find displacement and average velocity

Answer 1

Answer:

If the radius of the semicircular track is 5 meter then the displacement of the car will be equal to 2r. Displacement is the shortest distance travelled by the body from initial point to final point. According to the question, the shortest distance between the final point Q and Initial point P is PQ = 2r [See the figure which I've attached].

$\longrightarrow\:\: \rm Displacement = 2 \times Radius$

$\longrightarrow\:\: \rm Displacement = 2 \times 5$

$\longrightarrow\:\: \underline{ \underline{ \rm Displacement = 10 \: m }}$

Now, let's find the Average Velocity of the semicircular track.

$\longrightarrow\:\: \sf Average \: Velocity = \dfrac{Total \: Displacement}{Total \: Time}$

Here, distance travelled by an car in a semicircular track is equal to circumference of the semi circle.

$\longrightarrow\:\: \sf Average \: Velocity = \dfrac{10}{Total \: Time}$

$\qquad \qquad\footnotesize\bullet\:\sf Time = \dfrac{Distance}{Speed}$

$\longrightarrow\:\: \sf Average \: Velocity = \dfrac{10}{\dfrac{Distance}{Speed}}$

• Distance travelled by the car in semicircular track is equal to the circumference of the semicircle.
• Speed is given as π m/s.

$\longrightarrow\:\: \sf Average \: Velocity = \dfrac{10}{\dfrac{2\pi D}{\pi}}$

$\longrightarrow\:\: \sf Average \: Velocity = \dfrac{10}{\dfrac{2\pi \frac{r}{2} }{\pi}}$

$\longrightarrow\:\: \sf Average \: Velocity = \dfrac{10}{\dfrac{\pi r }{\pi}}$

$\longrightarrow\:\: \sf Average \: Velocity = \dfrac{10}{r}$

Radius of the semicircular track is 5 m :

$\longrightarrow\:\: \sf Average \: Velocity = \dfrac{10}{5}$

$\longrightarrow\:\: \underline{ \underline{ \sf Average \: Velocity = 2 \: {ms}^{ - 1}}}$