Question

The initial velocity of an object is \(\vec{u}=3\hat{i}+2\hat{j}\) m/s. Its constant acceleration is \(\vec{a}=5\hat{i}+3\hat{j}\) m/s\({}^{2}\). The magnitude of the final velocity after \(5\) s is

• A. \(\sqrt{573}\)
• B. \(\sqrt{873}\)
• C. \(\sqrt{1073}\)
• D. \(\sqrt{373}\)

Hint:

Treat v = u + at as a vector equation, add the components, then take the magnitude.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For constant acceleration the final velocity is \(\vec{v}=\vec{u}+\vec{a}t\).
Add the \(\hat{i}\) and \(\hat{j}\) components separately.

Step 2: Calculation of Components
\(v_x=3+5\times 5=28\) m/s
\(v_y=2+3\times 5=17\) m/s

Step 3: Magnitude
\(|\vec{v}|=\sqrt{28^{2}+17^{2}}=\sqrt{784+289}=\sqrt{1073}\) m/s

Step 4: Compare the options
\(\sqrt{1073}\) matches option (C).

Final Answer:
The magnitude of the final velocity is \(\sqrt{1073}\) m/s. \[ \boxed{\text{(C) }\sqrt{1073}} \]