Question

The position of body varies as \[ S = 9t^2 - 6t. \text{ What is the time at which the body becomes at rest?} \]

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

To find the time when an object becomes at rest, differentiate the position function to find the velocity, and set the velocity equal to zero.

Answer 1

The Correct Option is B

To find the time at which the body becomes at rest, we first calculate the velocity by differentiating the position function with respect to time: \[ v = \frac{dS}{dt} = 18t - 6 \] The body becomes at rest when \( v = 0 \), so: \[ 18t - 6 = 0 \quad \Rightarrow \quad t = \frac{6}{18} = 1 \] Thus, the time at which the body becomes at rest is \( t = 1 \).