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 maximum velocity, in \(\text{ms}^{-1}\), of the particle at \(B\).
\(4\dfrac{1}{16} \text{ ms}^{-1}\)
A particle moves along a straight line and passes through a fixed point \(O\).
Its velocity, \(v \text{ ms}^{-1}\), is given by
\(v=ht^2+kt,\)
where \(h\) and \(k\) are constants and \(t\) is the time, in seconds, after passing through \(O\).
It is given that the particle stops instantaneously when \(t=3 \text{ s}\) and its acceleration is \(-3 \text{ ms}^{-2}\) when \(t=1\text{ s}\).
Find the range of values of \(t\) when the particle moves to the left.
[Assume motion to the right is positive]
\(0 \lt t \lt 2\)
A particle moves from a fixed point \(O\) along a straight line.
\(v=2t^2-10t-72,\)
where \(t\) is the time in seconds after passing through \(O\).
Find the value of \(t\), in seconds, when the particle stops instantaneously.
\(8 \text{ s}\)
A particle moves along a straight line and passes through a fixed point \(O\) with a velocity of \(5 \text{ ms}^{-1}\).
The acceleration, \(a \text{ ms}^{-2}\), is given by
\(a=3t-9,\)
where \(t\) is the time, in seconds, after passing through the fixed point \(O\).
Find the initial acceleration, in \(\text{ms}^{-2}\), of the particle.
\(-9 \text{ ms}^{-2}\)
Its velocity, \(v \text{ ms}^{-1}, \) is given by
\(v=ht^2-5t\),
where \(h\) is a constant and \(t\) is the time in seconds after passing \(O\).
Acceleration of the particle is \(31 \text{ ms}^{-1}\) when \(t=2 \text{ s}\).
Find the value of \(h\).
\(7\)
There is something wrong with this question.
