Question

The velocity of a particle is given by \( V = 4t^3 - 5t^2 \). When does the acceleration of the particle become zero?

• A. 8.33 s
• B. 0.833 s
• C. 0.0833 s
• D. 1 s

Hint:

- Acceleration is the derivative of velocity, and setting it to zero gives instantaneous rest points.

Answer 1

The Correct Option is B

Step 1: Finding acceleration. - Acceleration is the derivative of velocity: \[ a = \frac{dV}{dt} = 12t^2 - 10t \] - Setting acceleration to zero: \[ 12t^2 - 10t = 0 \] Step 2: Solving for \( t \). \[ t(12t - 10) = 0 \] \[ t = 0, \quad t = \frac{10}{12} = 0.833 {s} \] Step 3: Selecting the correct option. Since acceleration is zero at \( t = 0.833 \)s, the correct answer is (B).