Question

A car is moving on a horizontal circular road of radius $100m$ with a uniform speed $10m/s$ . It suddenly accelerates at $1m/s^2$. The net acceleration of the car is:

• A. $1{m/s}^2$
• B. ${\sqrt{2}m/s}^2$
• C. $2{m/s}^2$
• D. ${\sqrt{5}m/s}^2$

Answer 1

The correct option is B ${\sqrt{2}m/s}^2$

When the car was moving with uniform speed, it has a centripetal acceleration.
Now, the car accelerates at $1m/s^2$.

So, the net acceleration of the car is

$a^{\prime }=\sqrt{(\frac{v^2}{r}{)}^2+a^2}=\sqrt{(\frac{{10}^2}{100}{)}^2+1^2}=\sqrt{1+1}=\sqrt{2}m/s^2$