Kinematics Question 157
Question: A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is
Options:
A) 4.0 m/s
B) 5.0 m/s
C) 5.5 m/s
D) 4.8 m/s
Show Answer
Answer:
Correct Answer: A
Solution:
[a] If $ t _{2} $ and $ 2t _{2} $ are the time taken by particle to cover first and second half distance, respectively, then $ t _{1}=\frac{x/2}{3}=\frac{x}{6} $
$ x _{1}=4.5t _{2} $ and $ x _{2}=7.5t _{2} $ So, $ x _{1}=x _{2}=\frac{x}{2}\Rightarrow 4.5t _{2}+7.5t _{2}=\frac{x}{2} $
$ t _{2}=-\frac{x}{24} $ Total time $ t _{1}+x _{2}+2t _{2}=\frac{x}{6}+\frac{x}{12}=\frac{x}{4} $ So, average speed 4 m/sec.
