Giúp mik nhanh vs ạ !!

Đáp án:

a) \({a_1} = 5\left( {m/{s^2}} \right)\) ; \({a_2} = 10\left( {m/{s^2}} \right)\)

b) \(\dfrac{{2\sqrt 5 }}{5}\left( s \right)\)

Giải thích các bước giải:

a) Ta có:

\(\begin{array}{l}
{s_2} = 2{s_1} \Rightarrow \dfrac{1}{2}{a_2}{t^2} = 2.\dfrac{1}{2}{a_1}{t^2} \Rightarrow {a_2} = 2{a_1}\\
{T_2} - {P_2} = {m_2}{a_2}\\
 \Rightarrow {T_2} - 5 = 0,5{a_2}\\
 \Rightarrow {T_2} - 0,5.2.{a_1} = 5\\
 \Rightarrow {T_2} - {a_1} = 5\\
{T_1} = {T_2}\\
{P_1} - {T_1} = {m_1}{a_1}\\
 \Rightarrow 20 - {T_2} = 2{a_1}\\
 \Rightarrow {T_2} + 2{a_1} = 20\\
 \Rightarrow \left\{ \begin{array}{l}
{T_2} = 10N\\
{a_1} = 5\left( {m/{s^2}} \right) \Rightarrow {a_2} = 10\left( {m/{s^2}} \right)
\end{array} \right.
\end{array}\)

b) Ta có: 

\(s = \dfrac{1}{2}{a_1}{t^2} \Rightarrow 2 = \dfrac{1}{2}.5.{t^2} \Rightarrow t = \dfrac{{2\sqrt 5 }}{5}\left( s \right)\)