Question

A car is moving on a circular track of radius of $150m$, and at some time, its speed is decreasing at a rate of $8m/s^2$. If the speed of the car at that instant was $30m/s$, then the net acceleration of the car will be

• A. $10m/s^2$
• B. $8m/s^2$
• C. $14m/s^2$
• D. $6m/s^2$

Answer 1

The correct option is A

$10m/s^2$

Step 1: Given

Translatory acceleration, $a_T=8m/s^2$

Radius, $r=150m$

Instant velocity, $v=30m/s$

Step 2: Formula used

Rotational acceleration is given by $a_r=\frac{v^2}{r}$.

Step 3: Find the rotational acceleration

$$\begin{gathered} a_r=\frac{v^2}{r} \\ =\frac{{30}^2}{150} \\ =6m/s^2 \end{gathered}$$

Step 4: Determine the net acceleration

$$\begin{gathered} \left|\overrightarrow{a}\right|=\sqrt{{\overrightarrow{\left|a_r\right|}}^2+{\overrightarrow{\left|a_T\right|}}^2} \\ =\sqrt{6^2+8^2} \\ =\sqrt{100} \\ =10m/s^2 \end{gathered}$$

Therefore, option A is the correct option.