Question

For a particle moving according to the equation \(x = a \cos \pi t\), the displacement in 3 s is

• A. 0
• B. \(0.5a\)
• C. \(1.5a\)
• D. \(2a\)
• E. \(a\)

Hint:

Always compute displacement as final minus initial, not distance.

Answer 1

The Correct Option is D

Concept: Displacement = final position - initial position.

Step 1: Initial position at \(t = 0\). \[ x_0 = a \cos 0 = a \]

Step 2: Position at \(t = 3\). \[ x_3 = a \cos (3\pi) \]

Step 3: Evaluate cosine. \[ \cos (3\pi) = -1 \Rightarrow x_3 = -a \]

Step 4: Find displacement. \[ \Delta x = x_3 - x_0 = (-a) - a = -2a \]

Step 5: Magnitude of displacement. \[ |\Delta x| = 2a \]

Step 6: Conclusion. \[ \boxed{2a} \]