The motion of a particle is described by the equation \(𝑥 = 𝑎 + 𝑏 𝑡^ 2\) where \(a = 15\ \text{cm}\) and \(b = 3\ \text{cm/s}^2\). Its instantaneous velocity at time \(3\) seconds will be:

1. \(36\ \text{cm/s}\)
2. \(18\ \text{cm/s}\)
3. \(16\ \text{cm/s}\)
4. \(32\ \text{cm/s}\)

A body travels for \(15\) seconds starting from rest with constant acceleration. If it travels distances \(S_1,\ S_2\) and \(S_3\) in the first five seconds, the second five seconds and the next five seconds, respectively, the relation between  \(S_1,\ S_2\) and \(S_3\) is:

1. \(𝑆_ 1 = 𝑆 _2 = 𝑆 _3\)
2. \(5𝑆_ 1 =3 𝑆 _2 = 𝑆 _3\)$\mathrm{}$
3. \(𝑆_ 1 = \frac 13 𝑆 _2 = \frac 15 𝑆 _3\)${}_{}$
4. \(𝑆_ 1 =\frac 15 𝑆 _2 = \frac 13 𝑆 _3\)${}_{}$

A body is moving according to the equation \(𝑥 = 𝑎 𝑡 + 𝑏 𝑡^ 2 − 𝑐 𝑡^ 3\) where \(x\) is the displacement, and \(a,\ b\) and \(c\) are constants. The acceleration of the body is:

1. \(𝑎 + 2 𝑏 𝑡\) 
2. \(2 𝑏 + 6 𝑐 𝑡  \)
3. \(2 𝑏 − 6 𝑐 𝑡  \)
4. \(3 𝑏 − 6 𝑐 𝑡^ 2  \)

A particle travels 10 m in first 5 sec and 10m in the next 3 sec. Assuming constant acceleration what is the distance travelled in next 2 sec ?

1. 8.3 m

2. 9.3 m

3. 10.3 m

4. None of above

The distance travelled by a particle is proportional to the square of time; then the particle travels with:

1. Uniform acceleration
2. Uniform velocity
3. Increasing acceleration
4. Decreasing velocity

The velocity of a particle changes when:

1. Direction of velocity changes
2. Magnitude of velocity changes
3. Both of above
4. None of the above

The motion of a particle is described by the equation \(u = at\), where \(u\) is the velocity and \(a\) is a constant. The distance travelled by the particle in the first \(4\) seconds:

1. \(4 a\)
2. \(12 a\)
3. \(6 a\)
4. \(8 a\)

The relation \(3t = \sqrt{3x} + 6\) describes the displacement of a particle in one direction where \(x\) is in metres and \(t\) in seconds. The displacement, when velocity is zero, is: 

The average velocity of a body moving with uniform acceleration travelling a distance of \(3.06\ \text{m}\) is \(0.34\ \text{ms}^{–1}\). If the change in velocity of the body is \(0.18\ \text{ms}^{–1}\) during this time, its uniform acceleration is:

1. \(0.01\ \text{ms}^{–2}\)

2. \(0.02\ \text{ms}^{–2}\)

3. \(0.03\ \text{ms}^{–2}\)

4. \(0.04\ \text{ms}^{–2}\)

The equation of displacement for any particle is \(𝑠 = 3 𝑡^ 3 + 7 𝑡^ 2 + 14 𝑡 + 8\ \text{m}\). Its acceleration at time \(t = 1\) second is:

1. \(10\ \text{m/s}^2\)
2. \(16\ \text{m/s}^2\)
3. \(25\ \text{m/s}^2\)
4. \(32\ \text{m/s}^2\)