A particle moves along a straight line such that its displacement, \(s \text{ m}\), is given by
\(s=2t+\dfrac{7}{4}t^2-\dfrac{t^3}{3},\)
where \(t\) is the time in seconds after passing \(O\).
The particle rests instantaneously at a point \(A\) and reaches maximum velocity at point \(B\).
Find the time, in seconds, of the particle at \(A\).
\(2\text{ s}\)
A particle moves along a straight line and passes through a fixed point \(O\).
Its velocity, \(v \text{ ms}^{-1}\), is given by
\(v=-t^2+2t+3\)
where \(t\) is the time in seconds after passing through \(O\).
The particle reaches a maximum velocity at point \(P\), changes its direction at point \(Q\) and passes through point \(R\) after \(4\) seconds.
Find the distance, in \(\text{m}\), of \(QP\).
[Assume motion to the right is positive]
\(4\dfrac{1}{3} \text{ m}\)
A particle moves along a straight line with an initial velocity of \(15 \text{ ms}^{-1}.\)
Its acceleration, \(a \text{ ms}^{-2}\), is given by
\(a=-3t+6,\)
where \(t\) is the time, in seconds, after passing through a fixed point \(O\).
Find the maximum velocity, in \(\text{ ms}^{-1},\) of the particle.
\(21 \text{ ms}^{-1}\)
Find the total distance, in \(\text{m}\), travelled by the particle from \(P\) to \(R\).
\(7\dfrac{2}{3}\text{ m}\)
\(a=-2t+2,\)
Find the displacement, in \(\text{m}\), when the particle stops instantaneously.
\(57\dfrac{1}{3} \text{ m}\)
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