A car is moving with speed 20 textm s- 1 on a circular path of radius 100 textm . Its speed is increasing at a rate of 3 textm s- 2 . The magnitude of the acceleration of the car at that moment is

Question

A car is moving with speed 20 textm s- 1 on a circular path of radius 100 textm . Its speed is increasing at a rate of 3 textm s- 2 . The magnitude of the acceleration of the car at that moment is (A) 1 textm s- 2 (B) 3 textm s- 2 (C) 4 textm s- 2 (D) 5 textm s- 2

Tardigrade Admin · Accepted Answer

Given v=20 textm s- 1 text, R = 100 textm (d v/d t)= text3 textm s- 2 ac=(v2/R)=((. 20 .)2/100)=4 ( textm s)- 2 at=(d v/d t)=3 textm s- 2 a=√ac2 + at2=√42 + 32=5 textm s- 2

Q. A car is moving with speed $20 m s^{- 1}$ on a circular path of radius $100 m$ . Its speed is increasing at a rate of $3 m s^{- 2}$ . The magnitude of the acceleration of the car at that moment is

$1 m s^{- 2}$

$3 m s^{- 2}$

$4 m s^{- 2}$

$5 m s^{- 2}$

Given $v = 20 m s^{- 1},$
$R = 100 m$
$\frac{d v}{d t} = 3 m s^{- 2}$
$a_{c} = \frac{v ^{2}}{R} = \frac{( 20 ) ^{2}}{100} = 4 (m s)^{- 2}$
$a_{t} = \frac{d v}{d t} = 3 m s^{- 2}$
$a = a_{c}^{2} + a_{t}^{2} = 4^{2} + 3^{2} = 5 m s^{- 2}$

Q. A car is moving with speed 20m s−1 on a circular path of radius 100m . Its speed is increasing at a rate of 3m s−2 . The magnitude of the acceleration of the car at that moment is

1m s−2

3m s−2

4m s−2

5m s−2