question_answer

Starting from rest a particle moves in a straight line with acceleration \[a={{(25-{{t}^{2}})}^{1/2}}m/{{s}^{2}}\] for \[0\le t\le \text{ }5s\], \[a=\frac{3\pi }{8}m/{{s}^{2}}\] for \[t>5s\]. The velocity of particle at \[t=7s\] is:

A) 11 m/s

B) 22 m/s

C) 33 m/s  

D) 44 m/s

Correct Answer: B

Solution :

\[{{V}_{7}}={{V}_{5}}+\frac{3\pi }{8}\times 2\] To calculate V5 i.e. velocity at end of 5 sec. \[a={{\left( 25-{{t}^{2}} \right)}^{{}^{1}/{}_{2}}}\Rightarrow \frac{dv}{dt}={{\left( 25-{{t}^{2}} \right)}^{{}^{1}/{}_{2}}}\]