Two mass points

Two mass points start moving simultaneously in the same direction from the same location: the first point uniformly with a speed of 50 cm/s, and the second point uniformly accelerated with zero initial speed and an acceleration of 10 cm/s².

Determine
a) the time it takes for both mass points to have the same speed
b) the time it takes for both mass points to travel the same path.

Correct answer:

t₁ =  5 s
t₂ =  10 s

Step-by-step explanation:

$$\begin{gathered} v_1=50\text{cm/s} \\ {v}_2=0\text{cm/s} \\ {a}_2=10{\text{cm/s}}^2 \\ {v}_1=a_2{t}_1 \\ {t}_1=v_1/a_2=50/10=5\text{s} \end{gathered}$$

$$\begin{gathered} v_1\cdot t_2=\frac{1}{2}\cdot a_2\cdot t_2 \\ 50t_2=0.5\cdot 10\cdot t_2^2 \\ 50=5\cdot t_2 \\ {t}_2=50/5=10\text{s} \end{gathered}$$

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