Velocity constant that stops a particle turning back
Velocity constant that stops a particle turning back
IP 4
9 marks
A particle moves in a straight line, starting from a fixed point \(O\). Its velocity, \(v\) m/s, \(t\) seconds after leaving \(O\) is \(v=3t^2-12t+c\), where \(c\) is a constant.
- Find the set of values of \(c\) for which the particle never moves back towards \(O\) for \(t\ge0\).[3]
- For \(c=9\), find the times at which the particle is at rest and the total distance travelled in the first \(4\) seconds.[4]
- For \(c=12\), show that the particle is instantaneously at rest at \(t=2\) but does not change direction there.[2]
Solution:
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Answer:(a) \(c\ge12\) (b) at rest at \(t=1\) and \(t=3\); distance \(12\) m (c) \(v=3(t-2)^2\ge0\), zero only at \(t=2\)
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