A particle has initial velocity \(\left(2 \hat{i} + 3 \hat{j}\right)\) and acceleration \(\left(0 . 3 \hat{i} + 0 . 2 \hat{j}\right)\). The magnitude of velocity after 10 sec will be:

1. \(9 \sqrt{2}   units\)

2. \(5 \sqrt{2}   units\)

3. 5 units

4. 9 unit

A particle has initial velocity $\left(3\hat{i}+4\hat{j}\right)$ and has acceleration $\left(0.4\hat{i}+0.3\hat{j}\right)$. Its speed after 10s is 

(1) 7unit                                                         

(2) 7$\sqrt{2}$unit

(3) 8.5 unit                                                     

(4) 10 unit

A particle starts from the origin \((0,0)\) at time \(t=0\) with an initial velocity of \(5\hat{j}\)​ m/s. It moves in the \(xy \text-\)plane under a constant acceleration of \((10 \hat{i}+4 \hat{j})\) m/s². At some instant, its coordinates are \((20~\text{m},~y_0~\text{m}).\) The value of \(y_0\) is:

The \(x,y\) components of the velocity of a particle moving in a plane are shown in the graphs.

 
The maximum velocity of the particle has the magnitude:
1. \(35~\text{m/s}\)
2. \(20\sqrt{3}~\text{m/s}\)
3. \(50~\text{m/s}\)
4. \(70~\text{m/s}\)

Starting from the origin at a time \(t = 0,\) with an initial velocity \(5\hat j~\text{ms}^{-1},\) a particle moves in the \((x\text-y)\) plane with a constant acceleration of \((10\hat i+4\hat j)~\text{ms}^{-2}.\) At time \(t,\) its coordinates are \((20~\text{m}, y_0~\text m).\) The value of \(t\) is:

A particle has initial velocity $\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right)$ and has acceleration $\left(0.4\hat{\mathrm{i}}+0.3\hat{\mathrm{j}}\right)$. Its speed after 10 s:

1. 7 units

2. $7\sqrt{2}$ units

3. 8.5 units

4. 10 units

A ball is dropped from the top of a tower of 100m height. Simultaneously another ball is thrown upwards from the bottom of the tower with a speed of 50 m/s ($g=10m/s^2$). They will cross each other after:

1. 1 s

2. 2 s

3. 3 s

4. 4 s

A body started moving with an initial velocity of \(4 ~\text{m/s}\) along the east and an acceleration of \(1~\text{m/s}^2\)${\mathrm{}}^{}$ along the north. The velocity of the body just after \(4 ~\text{s}\) is:

1. \(8~\text{m/s}\) along east
2. $\mathrm{}$\(4\sqrt{2} ~\text{m/s}\) along north-east
3. \(8~\text{m/s}\) along north
4. $\mathrm{}$\(4\sqrt{2} ~\text{m/s}\) along south-east