Body meeting

From two places, M and N, 100 m apart, two bodies move simultaneously in the positive direction of the x-axis. A body moving from place M has a speed of 5 m/s, from place N 3 m/s. How long does it take for the first body to catch up with the second? What path will the bodies travel in this time?

Final Answer:

t =  50 s
s₁ =  150 m
s₂ =  250 m

Step-by-step explanation:

$$\begin{gathered} v_1=3\text{m/s} \\ {v}_2=5\text{m/s} \\ s=100+v_1\cdot t \\ s=v_2\cdot t \\ 100+v_1\cdot t=v_2\cdot t \\ 100+3\cdot t=5\cdot t \\ 2t=100 \\ t=\frac{100}{2}=50 \\ t=50=50\text{s} \end{gathered}$$

$s_1=v_1\cdot t=3\cdot 50=150\text{m}$

$s_2=v_2\cdot t=5\cdot 50=250\text{m}$

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