2. A particle \(P\) moves in a straight line. At time \(t = 0 , P\) passes through a point \(O\) on the line. At time \(t\) seconds, the velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) where
- Find the acceleration of \(P\) when \(t = \frac { 1 } { 2 }\)
- Find the distance travelled by \(P\) in the interval \(0 \leqslant t \leqslant 1\)
At time \(t\) seconds, the velocity of \(P\) is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) where
$$v = ( 2 t - 1 ) ( 1 - t )$$
- Find the acceleration of \(P\) when \(t = \frac { 1 } { 2 }\)