Question

A motor car is moving with speed $30\, m\, s ^{-1}$ on a circular path of radius $500\, m$. Its speed is increasing at the rate of $2\, m\, s ^{-2},$ what will be its resultant acceleration?

• A. $2.5\, m\, s ^{-2}$
• B. $2.7 \,m \,s ^{-2}$
• C. $2\, m\, s ^{-2}$
• D. $4.5\, m\, s ^{-2}$

Answer 1

Answer: (B)

Centripetal acceleration,
$a_{c}=\frac{v^{2}}{r}=\frac{(30)^{2}}{500}=\frac{9}{5}=1.8\, m\, s ^{-2}$
Tangential acceleration, $a_{t}=2\, m\, s ^{-2}$
$\therefore $ Resultant acceleration,
$a=\sqrt{a_{c}^{2}+a_{t}^{2}}=\sqrt{(1.8)^{2}+2^{2}}=2.7\, m\, s \,{}^{-2}$