(i)[6]
Show that $v = 0.8e^{\frac{1}{2}x}$.
(ii)[4]
Determine the time taken for $P$ to move $1.4\,\text{m}$ from $O$.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A particle $P$ with mass $0.5\,\text{kg}$ travels along a straight line on a smooth horizontal plane. When the displacement of $P$ from $O$ is $x\,\text{m}$, its velocity is $v\,\text{m s}^{-1}$. A lone horizontal force of size $0.16e^{x}\,\text{N}$ acts on $P$ in the direction $OP$. The speed of $P$ at $O$ is $0.8\,\text{m s}^{-1}$.