A car is moving along a circular path of radius 500 m with a speed of 30 ms−1 . If at some instant, its speed increases at the rate of 2 ms−2 , then at that instant the magnitude of resultant acceleration will be

Question

A car is moving along a circular path of radius 500 m with a speed of 30 ms−1 . If at some instant, its speed increases at the rate of 2 ms−2 , then at that instant the magnitude of resultant acceleration will be (A)  4.7 ms−2  (B)  3.8 ms−2  (C)  3 ms−2  (D)  2.7 ms−2

Tardigrade Admin · Accepted Answer

Centripetal acceleration, ac=(v2/r)=((30)2/500)=1.8 ms -2 Tangential acceleration, at=2 ms -2 ∴ Resultant acceleration a=√at2+ac2 =√(1.8)2+(2)2 =2.7 ms -2

Q. A car is moving along a circular path of radius $500 m$ with a speed of $30 m s^{- 1}$ . If at some instant, its speed increases at the rate of $2 m s^{- 2}$ , then at that instant the magnitude of resultant acceleration will be

$4.7 m s^{- 2}$

$3.8 m s^{- 2}$

$3 m s^{- 2}$

$2.7 m s^{- 2}$

Centripetal acceleration,
$a_{c} = \frac{v ^{2}}{r} = \frac{( 30 ) ^{2}}{500} = 1.8 m s^{- 2}$
Tangential acceleration, $a_{t} = 2 m s^{- 2}$
$∴$ Resultant acceleration $a = a_{t}^{2} + a_{c}^{2}$
$= (1.8)^{2} + (2)^{2}$
$= 2.7 m s^{- 2}$

Q. A car is moving along a circular path of radius 500m with a speed of 30ms−1 . If at some instant, its speed increases at the rate of 2ms−2 , then at that instant the magnitude of resultant acceleration will be

4.7ms−2

3.8ms−2

3ms−2

2.7ms−2