Question

A cyclist is riding with a speed of $27km{h}^{-1}$. As he approaches a circular turn on the road of radius $80m$, he applies brakes and reduces his speed at the constant rate of $0.5m{s}^{-2}$. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

Answer 1

As the cyclist approaches the turn.

The tangential acceleration.

$a_T=0.5m/s^2$

and the radial acc,

$a_C=\frac{v^2}{r}=\frac{{7.5}^2}{80}=0.703m/s^2$

Thus total acc,

$a_{T=}\sqrt{a_c^2+a_r^2}=\sqrt{{0.5}^2+{0.703}^2}=0.8627m/s^2$

and the direction.

$tan\theta =\frac{a_T}{a_C}=\frac{0.5}{0.703}=0.711$

$\theta ={35.42}^0$