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અચળ બળ $\overrightarrow F = {F_x}\hat i + {F_y}\hat j$ હેઠળ એક $5\, kg$ દળનો પદાર્થ $t\,= 0\, s$ સમયે $\overrightarrow v = \left( {6\hat i - 2\hat j\,m/s} \right)$ જેટલો અને $t\, = 10\,s$ સમયે $\overrightarrow v = +6\hat j\,m/s$ જેટલો વેગ ધરાવે છે. તો બળ $\overrightarrow F $ કેટલું થશે?
$\left( { - 3\hat i + 4\hat j\,} \right)\,N$
$\left( { - \frac{3}{5}\hat i + \frac{4}{5}\hat j\,} \right)\,N$
$\left( {3\hat i - 4\hat j\,} \right)\,N$
$\left( {\frac{3}{5}\hat i - \frac{4}{5}\hat j\,} \right)\,N$
Solution
$\begin{array}{l}
From\,question,\\
Mass\,of\,body,\,m = 5\,kg\\
Vleocity\,at\,t = 0,\\
u = \,\left( {6\hat i – 2\hat j} \right)\,m/s\\
Velocity\,at\,t = 10s,\\
v = + 6\,\hat j\,m/s\\
Force,\,F = ?
\end{array}$
$\begin{array}{l}
Acceleration,\,a = \frac{{v – u}}{t}\\
= \frac{{6\hat j – \left( {6\hat i – 2\hat j} \right)}}{{10}} = – 3\hat i + 4\hat j\,m/{s^2}\\
Force,\,F = ma\\
= 5 \times \frac{{\left( {3\hat i + 4\hat j} \right)}}{5} = \left( { – 3\hat i + 4\hat j} \right)\,N
\end{array}$
