Question

A motor car is moving with the speed of $20m{s}^{-}1$ on a circular track of radius 100 m. If its speed is increasing at the rate of $3m{s}^{-}2$, the resultant acceleration is

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

Answer 1

The correct option is B $5m{s}^{-2}$

Given,

$a_t=3m/s^2$

$v=20m/s$

$r=100m$

Centripetal acceleration,

$a_c=\frac{v^2}{r}$

$a_c=\frac{20\times 20}{100}=4m/s^2$

The resultant acceleration,

$a=\sqrt{(a_t{)}^2+(a_c{)}^2}$

$a=\sqrt{(3{)}^2+(4{)}^2}=\sqrt{25}=5m/s^2$

The correct option is B.