Question

A race car moving on a circular track of radius 20 meters. If car’s speed is 108 km/h, then the magnitude of the centripetal acceleration is​

Answer 1

Answer :-

Centripetal acceleration of the car is 45 m/s² .

Explanation :-

We have :-

→ Radius of the circular track = 20 m

→ Speed of the car = 108 km/h

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Firstly, let's convert the speed of the car from km/h to m/s .

⇒ 1 km/h = 5/18 m/s

⇒ 108 km/h = 108(5/18)

⇒ 30 m/s

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Now we know that when a body is moving around a circular path, it's acceleration is given by :-

a꜀ = v²/r

Where :-

• a꜀ is acceleration of the body.

• v is speed of the body.

• r is radius of the circular path.

⇒ a꜀ = (30)²/20

⇒ a꜀ = 900/20

⇒ a꜀ = 45 m/s²

Answer 2

Answer:

Given :-

• A race car moving on a circular track of radius 20 metres.
• Car's speed is 108 km/h.

To Find :-

• What is the centrifugal acceleration.

Formula Used :-

$\clubsuit$ Centrifugal Acceleration Formula :

$\longmapsto \sf \boxed{\bold{\pink{a_c =\: \dfrac{v^2}{r}}}}$

where,

• $\sf a_c$ = Centrifugal Acceleration
• v = Velocity
• r = Radius

Solution :-

Given :

$\leadsto$ Radius :

$\implies \sf\bold{\green{20\: metres}}$

$\leadsto$ Velocity :

$\implies \sf 108\: km/h$

$\implies \sf 108 \times \dfrac{5}{18}$

$\implies \sf \dfrac{\cancel{540}}{\cancel{18}}$

$\implies \sf\bold{\green{30\: m/s}}$

Hence, we get :

• Radius (r) = 20 metres
• Velocity (v) = 30 m/s

According to the question by using the formula we get,

$\dashrightarrow \sf a_c =\: \dfrac{(30)^2}{20}$

$\dashrightarrow \sf a_c =\: \dfrac{30 \times 30}{20}$

$\dashrightarrow \sf a_c =\: \dfrac{90\cancel{0}}{2\cancel{0}}$

$\dashrightarrow \sf a_c =\: \dfrac{\cancel{90}}{\cancel{2}}$

$\dashrightarrow \sf\bold{\red{a_c =\: 45\: m/s^2}}$

$\therefore$ The centrifugal acceleration is 45 m/s².