A particle $P$ is travelling along a straight line, with displacement measured relative to a point

Question

A particle $P$ is travelling along a straight line, with displacement measured relative to a point $O$ on the line. The velocity, $v\text{ m s}^{-1}$, of the particle at time $t$ seconds is given by $v=\frac{1}{t+1}+e^{-t}$, where $t\geq0$. Find $\displaystyle ∫\left(\frac{1}{t+1}+e^{-t}\right)\,\mathrm{d}t$. Initially the particle is at $O$. Find an expression for the displacement, $s$ metres, in terms of $t$.

Accepted Answer

(a) $\ln(t+1)-e^{-t}+C$ (b) $s=\ln(t+1)-e^{-t}+1$

IB AA HL May 2026 P1 TZA Q2

IB AA HL May 2026 P1 TZA Q2

Solution:

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