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 interval with speed of $$4.5\ m/s$$ and $$7.5\ m/s$$ respectively. The average speed of the particle during this motion is

A
4.0 m/s
B
5.0 m/s
C
5.5 m/s
D
4.8 m/s

Solution

## The correct option is A $$4.0\ m/s$$$$\displaystyle t_{1}=\dfrac{\dfrac{S}{2}}{3}=\dfrac{S}{6}$$$$\displaystyle \dfrac{S}{2}=4.5\times t_{2}+7.5t_{3}\Rightarrow 12t_{2}=\dfrac{S}{2}$$We have $$t_2=t_3$$Total time $$\displaystyle t=t_{1}+t_{2}+t_3=\dfrac{S}{6}+\dfrac{S}{24}+\dfrac{S}{24}=\dfrac{S}{4}$$Average of $$\displaystyle \dfrac{S}{t}=\dfrac{S}{\dfrac{S}{4}}=4\: m/s$$Physics

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