Question

a car is travelling at 30 m/s on acircular road of radius 50m .it is increasing in speed at the rate of 2m/s² .it's acceleration is...?​

Answer 1

Given data :- A car is travelling at 30 m/s on a circular road of radius 50 m. It is increasing in speed at the rate of 2 m/s².

To find :- Car's acceleration ?

Solution :- According to given,

Here,

→ velocity of car = 30 m/s

→ radius of road = 50 m

Let, tangential acceleration be 2 m/s²

Now,

→ centripetal acceleration = v²/r

→ centripetal acceleration = (30)²/50

→ centripetal acceleration = 900/50

→ centripetal acceleration = 18 m/s²

Now, we need to calculate net acceleration:

$\bf{ \rightarrow{ a_{net} = \sqrt{ {a_{c}}^{2} + {a_{t}}^{2} } }}$

$\bf{ \rightarrow{ a_{net} = \sqrt{ {(18)}^{2} + {(2)}^{2} } }}$

$\bf{ \rightarrow{ a_{net} = \sqrt{ 324 + 4 } }}$

$\bf{ \rightarrow{ a_{net} = \sqrt{ 328} }}$

$\bf{ \rightarrow{ a_{net} = 2\sqrt{ 82 } \: \: m/{s}^{ 2} }}$

Hence, acceleration of car is 2√82 m/s².

{ Note :- 2√82 m/s² = 18.1107 m/s² }

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