A particle moves in a straight line with a fixed point $O$. The velocity of the particle, $v$ m/

Question

A particle moves in a straight line with a fixed point $O$. The velocity of the particle, $v$ m/s, is given by

\[v=\frac{25}{2t+1}+10\]

where $t$ is time in seconds after passing $O$.

Explain why the particle never change its direction of motion and will eventually travel at a speed close to 10 m/s.[2]
Find the acceleration of the particle at $t=2$.[2]
Calculate the distance travelled by the particle in the fifth second of its motion.[4]

Accepted Answer

(a) $v>0$ for $t\geq0$, so the particle never changes direction, and $v\to10\text{ m/s}$. (b) $-2\text{ m/s}^2$. (c) $12.5\text{ m}$ $(3\text{ s.f.})$.

2025 CHS PRELIMS P2 Q9

2025 CHS PRELIMS P2 Q9

Solution:

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