Question

A car is moving in a circular path of radius 500 m with a speed of 30 $ms^{-1}$. If the speed is increasing at the rate of 2 $ms^{-2}$ the resultant acceleration will be

• A. 2 $ms^{-2}$
• B. 2.5 $ms^{-2}$
• C. 2.7 $ms^{-2}$
• D. 4 $ms^{-2}$

Answer 1

Answer: (C)

2.7 $ms^{-2}$

Answer 2

Car will have two types of acceleration Radial acceleration, $a =\frac{v^2}{r} = \frac{30 \times 360}{500} = 1.8$ Tangential acceleration $a_r= 2\,ms^{-2}$ = Net acceleration $a = \sqrt{a_r^2 +a_r^2}$ = $\sqrt{(1.8)^2 + (2)^2 } = \sqrt{7.24}$ = 2.69 = 2.7 $ms^{-2}$