A particle $P$ moves in a straight line such that $t$ seconds after starting at displacemen

Question

A particle $P$ moves in a straight line such that $t$ seconds after starting at displacement $+1$ metre from $O$, its velocity, $v$ m/s, is given by $v = \frac{t^4}{16} - \frac{t^3}{6} - \frac{12t^2}{2} + C$. Find the equation determining the rest times in terms of $C$, explaining why numerical rest times cannot be specified, an expression for the displacement of the particle from $O$, displacement from $O$ at $t = 1$. The constant $C=v(0)$ is not assigned a numerical value. Express your answers in terms of $C$, with $t\ge0$.

Accepted Answer

The constant $C$ is undefined, so the rest time is not numerically determined. If the initial displacement is $1\text{ m}$, then (ii) $s=\dfrac{t^5}{80}-\dfrac{t^4}{24}-2t^3+Ct+1$; (iii) when $t=1$, $s=C-\dfrac{247}{240}$.

Kinematics - Finding the Equation of Displacement from Velocity

Kinematics - Finding the Equation of Displacement from Velocity

Solution:

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