The acceleration \(a\) (in ${\mathrm{ms}}^{-2}$) of a body, starting from rest varies with time \(t\) (in \(\mathrm{s}\)) as per the equation \(a=3t+4.\) The velocity of the body at time \(t=2\) \(\mathrm{s}\) will be:

A point moves in a straight line under retardation \(av^2\)${\mathrm{}}^{}$. If the initial velocity is \(u,\) the distance covered in \(t\) seconds is:
1. \((aut)\)

2. \(\dfrac{1}{a}\mathrm{ln}(aut)\)

3. \(\dfrac{1}{a}\mathrm{ln}(1+aut)\)

4. \(a~\mathrm{ln}(aut)\)

A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by \( ( 4 𝑡^ 3 − 2 𝑡 )\), where \(t\) is in sec and velocity in m/s. What is the acceleration of the particle when it is \(2\ \text{m}\) from the origin?

1. \(28\ \text{m/s}^2\)

2. \(22\ \text{m/s}^2\)

3. \(12\ \text{m/s}^2\)

4. \(10\ \text{m/s}^2\)

The velocity of a body depends on time according to the equation \(𝑣 = 20 + 0 .1 \ 𝑡^ 2\). The body is undergoing:

1. Uniform acceleration

2. Uniform retardation

3. Non-uniform acceleration

4. Zero acceleration

The displacement of a particle is given by \(y = a + bt + ct^{2} - dt^{4}\). The initial velocity and acceleration are, respectively: