A particle of mass $m$ moves along a straight line under the action of a force $F(x)=A-Bx$ (with $A,B0$) and a constant resistive force of magnitude $R$ opposing the motion. The particle starts from rest at $x=0$. Determine (i) the distance $x_{\max}$ at which the particle's speed is maximum, and (ii) the corresponding maximum speed $v_{\max}$, in terms of $A,B,R$ and $m$.

Question

A particle of mass $m$ moves along a straight line under the action of a force $F(x)=A-Bx$ (with $A,B>0$) and a constant resistive force of magnitude $R$ opposing the motion. The particle starts from rest at $x=0$. Determine (i) the distance $x_{\max}$ at which the particle's speed is maximum, and (ii) the corresponding maximum speed $v_{\max}$, in terms of $A,B,R$ and $m$.

Accepted Answer

x_max = (A - R)/B, v_max = (A - R)/sqrt(B m)

Gce Model Questions Vol1 2022 Further Mathematics Question 10

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