Question

A motor car is moving with a speed of $ 20\text{ }m{{s}^{-1}} $ on a circular track of radius $100 \,m$. If its speed is increasing at the rate of $ 3m{{s}^{-1}}, $ its resultant acceleration is

• A. $ 3\,m{{s}^{-2}} $
• B. $ 5\,m{{s}^{-2}} $
• C. $ 2.5\,m{{s}^{-2}} $
• D. $ 3.5\,m{{s}^{-2}} $
• E. $ 4\,m{{s}^{-2}} $

Answer 1

Answer: (B)

Resultant acceleration,
$ a=\sqrt{a_{c}^{2}+a_{t}^{2}} $
$ =\sqrt{\left( \frac{{{v}^{2}}}{r} \right)+{{(3)}^{2}}}=\sqrt{{{\left( \frac{20\times 20}{100} \right)}^{2}}+9} $
$ =\sqrt{16+9}=5\,m{{s}^{-2}} $