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1 of 8 0-day streak

Analyse displacement, velocity and a complete straight-line journey

Question 1 of 8

No calculator

Consider the motion of a point on a straight line. Time is measured in seconds, and displacement is measured in centimetres

\[x(t)=\frac{3}{2}\,t^{2} - 6\,t + 6\]

The stated time domain is shown below

\[t\in\left[0,5\right]\]

The table uses \(t=0\) and \(t=\frac{7}{2}\)

The table uses cm for displacement, cm/s for velocity and cm/s² for acceleration
\(t\)\(x(t)\)\(v(t)\)\(a(t)\)
\(0\)enter valueenter valueenter value
\(\frac{7}{2}\)enter valueenter valueenter value
(a)6 marks

Differentiate the displacement rule and complete the table

(b)1 mark

At \(t=\frac{7}{2}\), which direction is the point moving?

(c)1 mark

Which condition identifies a time when the point is at rest?