A particle has initial (t = 0) velocity u = 5i and is at origin

Question

A particle has initial (t = 0) velocity \(\vec{\mu}=5\hat {i}\) and is at origin at this instant. Its acceleration is given by \((3\hat {i}+4\hat {j}).\) When particle’s x co-ordinate is 16 units, then its speed is

(1) 13 units

(2) √161 units 

(3) 12 units 

(4) √185 units

Answer 1

(4) √185 units

\(S =ut + \frac {1}{2}at^2\)

⇒ \(16 = 5t +\frac {3}{2}t^2\)

⇒ t = 2

⇒ \(\vec {v}=\vec {u}+\vec {a}t = 11 \hat {i}+ 8\hat {j}\)