Question

The displacement of a particle at time \(t\) is \[ s = t^3 - 4t^2 - 5t \] Then the velocity of the particle at \(t = 2\) sec is

• A. \(\dfrac{1}{9}\) units/sec
• B. \(-9\) units/sec
• C. \(9\) units/sec
• D. \(-\dfrac{1}{9}\) units/sec

Hint:

Velocity is always obtained by differentiating displacement with respect to time.

Answer 1

The Correct Option is B

Step 1: Recall the definition of velocity.
Velocity is the rate of change of displacement: \[ v = \frac{ds}{dt} \]
Step 2: Differentiate \(s\) with respect to \(t\).
\[ v = 3t^2 - 8t - 5 \]
Step 3: Substitute \(t = 2\).
\[ v = 3(2)^2 - 8(2) - 5 = 12 - 16 - 5 = -9 \]