A particle is thrown upwards from the ground. It experiences a constant resistance force which can produce retardation of \(2~\text{m/s}^2\). The ratio of the time of ascent to the time of descent is: \([g = 10~\text{m/s}^2]\)
1. \(1:1\)
2. \(\sqrt{\frac{2}{3}}\)
3. \(\frac{2}{3}\)
4. \(\sqrt{\frac{3}{2}}\)

A bullet loses $\frac{1}{20}$ of its velocity passing through a plank. The least number of planks required to stop the bullet is (All planks offers same retardation)

(1) 10

(2) 11

(3) 12

(4) 23

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

1. 28 m/s²

2. 22 m/s²

3. 12 m/s²

4. 10 m/s²

The relation between time and distance is given by $$\(t=\alpha x^2+\beta x,\) where \(\alpha\) and \(\beta\) are constants. The retardation, as calculated based on this equation, will be (assume \(v\) to be velocity):
1. $\mathrm{}$\(2\alpha v^3\)
2. \(2\beta v^3\)$\mathrm{}{\mathrm{}}^{}$
3. \(2\alpha\beta v^3\)$\mathrm{}{\mathrm{}}^{}$
4. \(2\beta^2 v^3\)$\mathrm{}{\mathrm{}}^{}$

A point moves with uniform acceleration and v₁, v₂ and v₃ denote the average velocities in the three successive intervals of time t₁, t₂ and t₃. Which of the following relations is correct ?

(1) $(v_1-v_2):(v_2-v_3)=(t_1-t_2):(t_2+t_3)$

(2) $(v_1-v_2):(v_2-v_3)=(t_1+t_2):(t_2+t_3)$

(3) $(v_1-v_2):(v_2-v_3)=(t_1-t_2):(t_1-t_3)$

(4) $(v_1-v_2):(v_2-v_3)=(t_1-t_2):(t_2-t_3)$ 

The acceleration of a moving body can be found from: 

(1) Area under the velocity-time graph

(2) Area under the distance-time graph

(3) Slope of the velocity-time graph

(4) Slope of the distance-time graph

The initial velocity of a particle is u (at t = 0) and the acceleration f is given by at. Which of the following relation is valid 

1. $v=u+a{t}^2$

2. $v=u+a\frac{t^2}{2}$

3. $v=u+at$

4. v = u

The initial velocity of the particle is 10 m/sec and its retardation is 2 m/sec². The distance moved by the particle in 5^th second of its motion is 

(1) 1 m

(2) 19 m

(3) 50 m

(4) 75 m

A motor car moving with a uniform speed of 20 m/sec comes to stop on the application of brakes after travelling a distance of 10 m. Its acceleration is 

(1) 20 m/sec²

(2) –20 m/sec²

(3) –40 m/sec²

(4) +2 m/sec²

The velocity of a body moving with a uniform acceleration of 2 m/sec² is 10 m/sec. Its velocity after an interval of 4 sec is 

(1) 12 m/sec

(2) 14 m/sec

(3) 16 m/sec

(4) 18 m/sec