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.
Show Hint
- \( 1 \, \text{s} \)
\( 6 \, \text{s} \)
- \( 2 \, \text{s} \)
- \( 4 \, \text{s} \)
The Correct Option is B
Solution and Explanation
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 \( 6 \, \text{s} \).
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