Question

A car is moving with speed 27 km/h. The driver applies brakes as he approaches a circular turn on the road of radius 80 m and his speed reduce at the constant rate of 0.50 m/s every second. The magnitude of net acceleration is:

• A. $20m{s}^{-2}$
• B. $250m{s}^{-2}$
• C. $100m{s}^{-2}$
• D. None of these

Answer 1

The correct option is D None of these

Speed of cyclist$=27km/h$

$=27\times \frac{1000}{3600}$

$=7.5m/s$

Radius of track $=80m$

Centripetal acceleration $a=\frac{v^2}{r}$

$\Rightarrow a_c={\left(7.5\right)}^2/80=0.7m/s^2$

Tangential acceleration $a_t=0.5m/s^2$

Net acceleration

$a=\sqrt{{a_t}^2+{a_t}^2}=\sqrt{{\left(0.5\right)}^2+{\left(0.7\right)}^2}=0.8m/s^2$