Question

A motor car is traveling at $30m/s$ on a circular road of radius $500m$. It is increasing its speed at the rate of $2m/s^2$. What is its acceleration?

• A. $3.0m/s^2$
• B. $2.7m/s^2$
• C. $1.8m/s^2$
• D. $2.5m/s^2$

Answer 1

Answer: (B)

$2.7m/s^2$

Note that this is a case of circular motion so there will be 2 kinds of accelerations involved :
1) Tangential acceleration
2) Radial acceleration

The net acceleration will be the vector sum of the 2 accelerations

Now we know that radial acceleration = $\frac{v^2}{R}$

Where $v$ = speed and $R$ = radius of the circle

So, radial acceleration = $\frac{30\times 30}{500}$ = $\frac{9}{5}m/s^2$

Now we observe that the tangential acceleration and radial acceleration are mutually perpendicular vectors, so the angle between them is ${90}^0$.

So, net acceleration = $\sqrt{2^2+(\frac{9}{5}{)}^2}$

$=2.7m/s^2$