Question

A cyclist is moving with a speed of $6ms^{- 1}$ . As he approaches a circular turn on the road of radius $120m$ , he applies brakes and reduces his speed at a constant rate of $0.4ms^{- 2}$ . The magnitude of the net acceleration of the cyclist on the circular turn just after brakes is

• A. $0.5ms^{- 2}$
• B. $1.0ms^{- 2}$
• C. $2.0ms^{- 2}$
• D. $4.0ms^{- 2}$

Answer 1

Answer: (A)

It is a type of non-uniform circular case, so it has both radial $\left(a_{c}\right)$ and tangential acceleration $\left(a_{t}\right)$ , and net acceleration $\left(a_{n e t}\right)$ is the vector sum of both acceleration,
$a_{t}=0.4ms^{2}$
$a_{c}=\frac{F}{m}$
$a_{c}=\frac{m v^{2}}{m r}$
$a_{c}=\frac{v^{2}}{r}\Rightarrow \frac{6^{2}}{120}\Rightarrow 0.3ms^{- 2}$
$a_{n e t}=\sqrt{a_{c}^{2}+a_{t}^{2}}=\sqrt{(0.3)^{2}+(0.4)^{2}}=0.5$