Question

If the displacement of a particle at time \(t\) is given by \[ s = 3t^2 - 12t + 14, \] then the displacement of the particle when its velocity becomes zero is

• A. 14 units
• B. 4 units
• C. 0 units
• D. 2 units

Hint:

To find displacement at zero velocity, always differentiate the displacement function first and then substitute the time obtained back into the original equation.

Answer 1

The Correct Option is D

Step 1: Find the velocity of the particle.
Velocity is the rate of change of displacement with respect to time.
\[ v = \frac{ds}{dt} = \frac{d}{dt}(3t^2 - 12t + 14) = 6t - 12 \] Step 2: Set velocity equal to zero.
When the velocity becomes zero,
\[ 6t - 12 = 0 \Rightarrow t = 2 \] Step 3: Find displacement at \(t = 2\).
Substitute \(t = 2\) in the displacement equation:
\[ s = 3(2)^2 - 12(2) + 14 = 12 - 24 + 14 = 2 \] Step 4: Final conclusion.
The displacement of the particle when its velocity becomes zero is \(2\) units.