Magnitude of Instantaneous Velocity

Q.

The coordinates of a moving particle at any time are given by $x=a{t}^2$ and $y=b{t}^2$. The speed of the particle at any moment is

1. 2t(a + b)

2. $2t\sqrt{(a^2-b^2)}$

3. $t\sqrt{(a^2+b^2)}$

4. $2t\sqrt{(a^2+b^2)}$

Q. A body changes direction by an angle a, without changing speed (v). Change in magnitude of velocity is

1. zero
2. 2v sin a/2
3. v sin a/2
4. v sin a

Q. Two cars P and Q starts from a point at the same time in a straight line and their positions are represented by $x_p\left(t\right)=at+b{t}^2$ and $x_Q\left(t\right)=ft-t^2$. At what time do the cars have the same velocity?

1. $\frac{f-a}{2(1+b)}$
2. $\frac{a-f}{1+b}$
3. $\frac{a+f}{2(b-1)}$
4. 
   $\frac{a+f}{2(1+b)}$