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A particle travels along a straight line with speed \(v\) (in m/s) given by \(v=t^2+3t-4\), where \(t\) is in seconds. At what time does the particle momentarily stop?

1. t = 1 s
2. t = 2 s
3. t = 3 s
4. t = 4 s

Correct answer: t = 1 s

Solution

The particle stops when \(v=0\). Solving \(t^2+3t-4=0\) gives \((t+4)(t-1)=0\), so \(t=1\,\text{s}\) or \(t=-4\,\text{s}\). Since time cannot be negative here, the valid answer is \(1\,\text{s}\).

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