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

The gravity in space is given by $\overrightarrow{\mathrm{g}}=-10 \hat{j} m{s}^{-2}$. Two particles are simultaneously projected with velocity $\overrightarrow{{\mathrm{u}}_1}=\left(10 m{s}^{-1}\right)\hat{i}+\left(10 m{s}^{-1}\right)\hat{j}$ and $\overrightarrow{{\mathrm{u}}_2}=\left(20 m{s}^{-1}\right)\hat{i}+\left(10 m{s}^{-1}\right)\hat{j}$. Then, the ratio of their times of flight

1. 1:1

2. 1:2

3. 2:1

4. none

A train is moving towards the east and a car is along the north at the same speed. The observed direction of the car to the passenger on the train is:

Two racing cars of masses \(m_1\) and \(m_2\) are moving in circles of radii \(r_1\) and \(r_2\) respectively. Their speeds are such that each makes a complete circle in the same duration of time \(t\). The ratio of the angular speed of the first to the second car is:

A particle P is moving in a circle of radius ‘a’ with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio 

1. 1 : 1

2. 1 : 2

3. 2 : 1

4. 4 : 1

Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is 

1. R/r

2. r/R

3. R²/r²

4. r²/R²

An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m, the acceleration of a point on the tip of the blade is about

1. 1600 m/sec²

2. 4740 m/sec²

3. 2370 m/sec²

4. 5055 m/sec²

A particle moves with constant speed \(v\) along a circular path of radius \(r\) and completes the circle in time \(T\). The acceleration of the particle is:
1. \(2\pi v / T\)
2. \(2\pi r / T\)
3. \(2\pi r^2 / T\)
4. \(2\pi v^2 / T\)

If a_r and a_t represent radial and tangential accelerations, the motion of a particle will be uniformly circular if:
1. a_r = 0 and a_t = 0
2. a_r = 0 but a_t \(\neq\) 0
3. a_r \(\neq\) 0 but a_t = 0
4. a_r \(\neq\) 0 and a_t \(\neq\) 0$\mathrm{}$
 

The figure shows a body of mass m moving with a uniform speed v along a circle of radius r. The change in velocity in going from A to B is:

1. $v\sqrt{2}$

2. $v/\sqrt{2}$

3. v

4. zero