The motion of a particle is described by the equation $x=a+b{t}^2$ where a = 15 cm and b = 3 cm/s². Its instantaneous velocity at time 3 sec will be 

(1) 36 cm/sec

(2) 18 cm/sec

(3) 16 cm/sec

(4) 32 cm/sec

A body is moving according to the equation $x=at+b{t}^2-c{t}^3$ where x = displacement and a, b and c are constants. The acceleration of the body is 

(1) $a+2bt$ 

(2) $2b+6ct$ 

(3) $2b-6ct$ 

(4) $3b-6c{t}^2$ 

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 squares of time, then the particle travels with  

(1) Uniform acceleration

(2) Uniform velocity

(3) Increasing acceleration

(4) Decreasing velocity

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 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 m is 0.34 ms^–1. If the change in velocity of the body is 0.18ms^–1 during this time, its uniform acceleration is 

(1) 0.01 ms^–2

(2) 0.02 ms^–2

(3) 0.03 ms^–2

(4) 0.04 ms^–2

Equation of displacement for any particle is $s=3t^3+7t^2+14t+8m$. Its acceleration at time t = 1 sec is 

1. 10 m/s²

2. 16 m/s²

3. 25 m/s²

4. 32 m/s²  

The position of a particle moving along the x-axis at certain times is given below :

Which of the following describes the motion correctly?  

(1) Uniform, accelerated

(2) Uniform, decelerated

(3) Non-uniform, accelerated

(4) There is not enough data for generalization