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A particle moves along a straight line with constant acceleration. It passes through a point \(A\) with velocity \(u\) m s\(^{-1}\) and then through a point \(B\) with velocity \(v\) ms\(^{-1}\).
The velocity of the particle at the midpoint of the line segment \(AB\) is given by
\(D\)
\(\text{Let} \ \ u=\text{velocity at}\ A, \ v=\text {velocity at} \ B\)
\(v^2=u^2+2 a s \ \Rightarrow \ 2 a s=v^2-u^2\ \ldots\ (1)\)
\(\text{At halfway point:}\)
\(v_m^2=u^2+2 a \times \dfrac{s}{2}\)
\(\text {Using (1) above:}\)
\(v_m^2=u^2+\frac{1}{2}\left(v^2-u^2\right)=\dfrac{u^2+v^2}{2}\)
\(\Rightarrow D\)
A particle moving in a straight line with constant acceleration has a velocity of 7 ms\(^{-1}\) at point \(A\) and 17 ms\(^{-1}\) at point \(B\).
The velocity of the particle, in metres per second, at the midpoint of \(AB\) is
\(D\)
\(\text{Using}\ \ v^2=u^2+2as:\)
| \(17^2\) | \(=7^2+2as\) | |
| \(as\) | \(=120\) |
\(\text{Displacement (halfway)}\ = \dfrac{s}{2} \)
| \(v^2\) | \(=7^2+2a \times \dfrac{s}{2} \) | |
| \(=49+120\) | ||
| \(=169\) | ||
| \(\therefore v\) | \(=13\) |
\(\Rightarrow D\)