Average Velocity in 2D Motion

Q. A particle has initial velocity $(2\hat{i}+3\hat{j})$ and acceleration $(0.3\hat{i}+0.2\hat{j})$. The magnitude of velocity after $10\text{s}$ will be

1. $5units$
2. $9units$
3. $9\sqrt{2}units$
4. $5\sqrt{2}units$

Q. A particle is projected from the ground with an initial speed of $v$ at an angle $\theta$ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is

1. $\frac{v}{2}\sqrt{1+2{\cos }^2\theta }$
2. $\frac{v}{2}\sqrt{1+{\cos }^2\theta }$
3. $\frac{v}{2}\sqrt{1+3{\cos }^2\theta }$
4. $v\cos \theta$

Q. A particle is projected from the ground with an initial speed of $v$ at an angle $\theta$ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is

1. $\frac{v}{2}\sqrt{1+2{\cos }^2\theta }$
2. $\frac{v}{2}\sqrt{1+{\cos }^2\theta }$
3. $\frac{v}{2}\sqrt{1+3{\cos }^2\theta }$
4. $v\cos \theta$

Q.

A train moves at a constant speed of 60.0 km/h towards east for 30 min, then in a direction ${30}^{\circ }$ east of due north for 20.0 min, and then west for 45 min. What are the (a) magnitude(in km/min) and (b) angle of its average velocity during this trip?

1. Magnitude=$\left(\frac{19}{\sqrt{13}}\right);ta{n}^{-1}\left(\frac{-\sqrt{3}}{2}\right)$

2. Magnitude= $\frac{\sqrt{13}}{19};ta{n}^{-1}(-2\sqrt{3})$

3. Magnitude=$\left(\frac{\sqrt{13}}{19}\right);ta{n}^{-1}\left(2\sqrt{3}\right)$

4. Magnitude=$\frac{19}{\sqrt{13}};ta{n}^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Q.

A train moves at a constant speed of 60.0 km/h towards east for 30 min, then in a direction ${30}^{\circ }$ east of due north for 20.0 min, and then west for 45 min. What are the (a) magnitude(in km/min) and (b) angle of its average velocity during this trip?

1. Magnitude=$\left(\frac{19}{\sqrt{13}}\right);ta{n}^{-1}\left(\frac{-\sqrt{3}}{2}\right)$

2. Magnitude= $\frac{\sqrt{13}}{19};ta{n}^{-1}(-2\sqrt{3})$

3. Magnitude=$\left(\frac{\sqrt{13}}{19}\right);ta{n}^{-1}\left(2\sqrt{3}\right)$

4. Magnitude=$\frac{19}{\sqrt{13}};ta{n}^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Q. For an X-Y plot of a body undergoing 2D motion, the direction of average velocity between two given points, is always in the direction of displacement.

1. True
2. False