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} $

Answer 1

Answer: (D)

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