Moderate -0.8 This is a straightforward integration question requiring students to integrate a quadratic velocity function and use an initial condition to find the constant. It's a standard mechanics/calculus exercise with clear steps: integrate v to get s, substitute t=1 and s=-4 to find C, making it easier than average but not trivial.
A particle moves along the horizontal \(x\)-axis so that its velocity \(v\) ms\(^{-1}\) at time \(t\) seconds is given by
$$v = 6t^2 - 8t - 5.$$
At time \(t = 1\), the particle's displacement from the origin is \(-4\) m. Find an expression for the displacement of the particle at time \(t\) seconds. [3]
A particle moves along the horizontal $x$-axis so that its velocity $v$ ms$^{-1}$ at time $t$ seconds is given by
$$v = 6t^2 - 8t - 5.$$
At time $t = 1$, the particle's displacement from the origin is $-4$ m. Find an expression for the displacement of the particle at time $t$ seconds. [3]
\hfill \mbox{\textit{WJEC Unit 2 2018 Q07 [3]}}