Question

The displacement of a body varies with time $ t $ as $ S = \frac{1}{2} t^2 - 6t $. Find the time at which the velocity becomes zero.

• A. \( 1 \, \text{s} \)
• B. \( 6 \, \text{s} \)
• C. \( 2 \, \text{s} \)
• D. \( 4 \, \text{s} \)

Hint:

To find the time when the velocity is zero, differentiate the displacement equation to find the velocity equation and set it equal to zero.

Answer 1

The Correct Option is B

The displacement is given by: \[ S = \frac{1}{2} t^2 - 6t \] To find the time at which the velocity is zero, we first find the velocity by differentiating the displacement with respect to time: \[ v = \frac{dS}{dt} = t - 6 \] Now, set \( v = 0 \) to find when the velocity becomes zero: \[ 0 = t - 6 \] Solving for \( t \): \[ t = 6 \, \text{s} \] 
Thus, the time at which the velocity becomes zero is \( 6 \, \text{s} \).