A man weighing 80 kg is standing in a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley with a speed of 1 m/s, then after 4 sec his displacement relative to the ground will be

1. 5  m

2. 4.8 m

3. 3.2 m

4. 3.0 m

A particle is projected at an angle \(𝜃  \) with the horizontal with an initial speed \(u\). When it makes an angle \(𝛼\) with the horizontal, its speed \(v\) is:
1. \(𝑢 \cos 𝜃\)

2. \(𝑢 \cos 𝜃 \ 𝑢 \cos 𝛼 \)

3. \(\dfrac{u\sin \theta}{\sin \alpha}\)

4. \(\dfrac{u\cos \theta}{\cos \alpha}\)

A particle is moving along the path y = ${\mathrm{x}}^2$ from x = 0 m to x = 2 m. Then the distance traveled by the particle is:

1.  4 m

2.  $\sqrt{20}<mspace\; width="1em"></mspace>\mathrm{m}$

3.  $>\sqrt{20}<mspace\; width="1em"></mspace>\mathrm{m}$

4.  $<\sqrt{20}<mspace\; width="1em"></mspace>\mathrm{m}$

In a uniform circular motion, which of the following quantity is not constant

1. Angular momentum

2. Speed

3. Kinetic energy

4. Momentum

A particle is moving with velocity \(\vec v=k(y\hat i+x \hat j)\), where \(k\) is constant. The general equation for the path is:

1. \(y=x^2+\text{constant}\)

2. \(y^2=x^2+\text{constant}\)${\mathrm{}}^{}$

3. \(y=x+\text{constant}\)$\mathrm{}$

4. \(xy=\text{constant}\)

A projectile is given an initial velocity of \(\hat i+2\hat j\). The cartesian equation of its path is: (Take \(g = 10 \ \text{ms}^{ - 2}\)) 

1. \(y=2x-5x^2\)

2. \(y=x-5x^2\) $\mathrm{}$

3. \(4y=2x-5x^2\)$\mathrm{}$

4. \(y=2x-25x^2\)

The time taken by the projectile to reach from \(A\) to \(B\) is \(t\). Then the distance \(AB\) is equal to :

1. \(\dfrac{ut}{\sqrt3}\)

2. \(\dfrac{\sqrt3ut}{2}\)

3. \(\sqrt3ut\)

4. \(2ut\)

A particle starts from the origin at \(t=0\) and moves in the \(x-y\) plane with constant acceleration \(a\) in the \(y\) direction. Its equation of motion is \(  𝑦 = 𝑏 𝑥^2\). The \(x\) component of its velocity \((\text{at} \ t=0) \) is:

1. Variable

2. \(\sqrt{\dfrac{2a}{b}}\)

3. \(\dfrac{a}{2b}\)

4. \(\sqrt{\dfrac{a}{2b}}\)

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

What determines the nature of the path followed by the particle?

1. Speed only

2. Velocity only

3. Acceleration only

4. None of these