Question

A motor car is moving at 40 m/s on a circular road of radius 400 m. If its speed is increasing at the rate of 3 m/s², then its acceleration is:

• A. \( 3 \, {m/s}^2 \)
• B. \( 2.7 \, {m/s}^2 \)
• C. \( 5 \, {m/s}^2 \)
• D. \( 3.3 \, {m/s}^2 \)

Hint:

For circular motion, always remember to consider both centripetal and tangential accelerations when calculating total acceleration.

Answer 1

The Correct Option is C

The car is moving on a circular path, so it experiences both tangential and centripetal acceleration. 
Step 1: Centripetal acceleration The centripetal acceleration is given by the formula: \[ a_c = \frac{v^2}{r} \] where \( v = 40 \, {m/s} \) and \( r = 400 \, {m} \). Substituting the values: \[ a_c = \frac{(40)^2}{400} = 4 \, {m/s}^2. \] 
Step 2: Total acceleration The total acceleration is the sum of the tangential and centripetal accelerations: \[ a_{{total}} = \sqrt{a_t^2 + a_c^2} \] where \( a_t = 3 \, {m/s}^2 \) is the tangential acceleration. Substituting the values: \[ a_{{total}} = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, {m/s}^2. \] Thus, the total acceleration is \( 5 \, {m/s}^2 \).