Question

A car is travelling at \(30 \, \text{ms}^{-1}\) speed on a circular road of radius \(300 \, \text{m}\). If its speed is increasing at the rate of \(4 \, \text{ms}^{-2}\), then its acceleration is:

• A. \(2.7 \, \text{ms}^{-2}\)
• B. \(3 \, \text{ms}^{-2}\)
• C. \(4 \, \text{ms}^{-2}\)
• D. \(5 \, \text{ms}^{-2}\)

Hint:

When dealing with motion on a circular path where speed is changing, always combine centripetal and tangential accelerations using the Pythagorean theorem.

Answer 1

The Correct Option is D

Step 1: Identify the types of acceleration.
There are two types of acceleration here: \begin{itemize} \item Centripetal (radial) acceleration: \( a_c = \frac{v^2}{r} = \frac{30^2}{300} = 3 \, \text{ms}^{-2} \) \item Tangential acceleration (due to change in speed): \( a_t = 4 \, \text{ms}^{-2} \) \end{itemize}
Step 2: Find the net acceleration.
These accelerations are perpendicular to each other, so total acceleration is given by: \[ a = \sqrt{a_c^2 + a_t^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{ms}^{-2} \]