Position \(x\) of a particle moving on a straight line as a function of time \(t\) is \(x =(2t^{2}-12t+5) \text{ m}.\) The particle will come to rest at time \(t\) equal to:
1. \(2\) s
2. \(1\) s
3. \(4\) s
4. \(3\) s

The position of an object moving along the \(x\text-\)axis is described by:
        \(x=(a+bt^2 ),\)
where \(a=10\text{ m},\) \(b=2\text{ m/s}^2,\) and \(t\) is measured in seconds. What is the velocity of the object at \(t=3.0\text{ s}\text{?}\)

The coordinates of a moving particle at any time \(t\) are given by; \(x=\alpha t^3,\) and \(y=\beta t^3.\) The speed of the particle at time \(t\)  is given by:
1. \(\sqrt{(\alpha^2+\beta^2)}\)

2. \(3t \sqrt{(\alpha^2+\beta^2)}\)

3. \(3t^2 \sqrt{(\alpha^2+\beta^2)}\)

4. \(t^2 \sqrt{(\alpha^2+\beta^2)}\)

Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by; \(x_p(t)= at+bt^2\) and \(x_Q(t) = ft-t^2. \) At what time do the cars have the same velocity?