kinematics, examples, solved and unsolved problems, concept, kinematics pdf download

kinematics formula, examples, and kinematics problems along with kinematics concepts

Kinematics is a branch of mechanics that defines the motion of points, bodies (objects), and systems of bodies (groups of objects) while not considering the mass of every of the forces that caused the motion.

Kinematics is the mathematical description of motion. The term is derived from the Greek word kinema, meaning movement. In order to quantify motion,

a mathematical frame of reference, referred to as a arrangement, is used to describe space and time. Once a arrangement has been chosen, we will introduce the physical ideas of position, velocity and acceleration in a mathematically precise manner. The figure shows a co-ordinate system in one dimension with unit vector ˆi inform within the direction of skyrocketing x -coordinate.

Figure: A one-dimensional Cartesian coordinate system.

IMPORTANT TERMS:-

Speed: The speed of a body could also be outlined as its rate of amendment of displacement with reference to its surroundings. The speed of a body is regardless of its direction and is, thus, a scalar amount.

Velocity: the rate of a body could also be outlined as its rate of amendment of displacement, with reference to its surroundings, in a particular direction. As the speed is often expressed in an exceedingly explicit direction, thus it's a vector amount.

Acceleration: The acceleration of a body could also be outlined because the rate of amendment of its speed. It is said to be positive, when the velocity of a body increases with time, and negative when the velocity decreases with time. The negative acceleration is also called retardation. In general, the term acceleration is employed to denote the speed at that the rate is dynamical. It may be uniform or variable.

Uniform acceleration: If a body moves in such a way that its velocity changes in equal magnitudes in equal intervals of time, it is said to be moving with a uniform acceleration

Variable acceleration: If a body moves in such a way, that its velocity changes in unequal magnitudes in equal intervals of time, it is said to be moving with a variable acceleration.

Distance traversed: It is the total distance moved by a body. Mathematically, if body is moving with an even speed (v), then in (t) seconds, the distance traversed

S = v X t

In this chapter, we tend to shall discuss the motion beneath uniform acceleration solely.

  MOTION UNDER UNIFORM ACCELERATION

           

Consider the *linear motion of a particle ranging from O and moving on OX with an even acceleration as shown in Fig. 17.1. Let P be its position after t seconds.

Let u = Initial velocity,

v = Final velocity,

t = Time (in seconds) taken by the particle to alter its speed from u to v.

a = Uniform positive acceleration, and

s = Distance travelled in t seconds.

Since in t seconds, the velocity of the particle has increased steadily from (u) to (v) at the rate of a, therefore total increase in velocity = a t

∴ v = u + a t ... (i)

MOTION UNDER FORCE OF GRAVITY

It is a specific case of motion, under a constant acceleration of (g) where it’s value is taken as 9.8 m/s2. If there's a free be gravity, the expressions for velocity and distance travelled in terms of initial velocity, time and gravity acceleration will be:

But, if the motion takes place against the force of gravity, i.e., the particle is projected upwards, the corresponding equations will be:

Notes: 1. In this case, the value of u is taken as negative due to upward motion.

2. During this case, the distances in upward direction area unit taken as negative, while those in the downward direction are taken as positive.

Distance Traveled in nth second

GRAPHICAL REPRESENTATION OF VELOCITY, TIME AND DISTANCE TRAVELLED BY A BODY

The motion of body may be portrayed by suggests that of a graph. Such a graph could also be drawn by plotting speed as ordinate and therefore the corresponding time as Cartesian coordinate as shown in Fig.

17.5. (a) and (b). Here we tend to shall discuss the subsequent 2 cases:

1. When the body is moving with a uniform velocity.

Consider the motion of a body, which is represented by the graph OABC as shown in Fig. 17.5(a). We know that the distance traversed by the body,

s = Velocity × Time

Thus we tend to see that the world of the figure OABC (i.e., velocity × time) represents the distance,

2. When the body is moving with a variable velocity

We know that the distance traversed by a body, traversed by the body, to some scale.

S= ut + 1/2 at²

From the geometry of the Fig. 17.5 (b),

We know that area of the figure OABC = Area (OADC + ABD)

But space of figure OADC = u × t

And

Area of figure ABD = 1/2 × t × at =1/2 at²

∴ Total area OABC = S=ut+1/2 at²

Thus, we tend to see that the world of the OABC represents the space traversed by the body to some scale. From the figure, it is also seen

tan α = at/t = a

Thus, tan α represents the acceleration of the body.

Example:- A train moving with a velocity of 30 km.p.h. has to slow down to 15 km.p.h. due to repairs along the road. If the distance covered during retardation be one kilometer and that covered throughout acceleration be [*fr1] a kilometer, find the time lost in the journey.

                        ∴ Total time, t = t₁ + t₂ = 2.67 + 1.33 = 4 min

If the train had enraptured uniformly with a speed of thirty km/hr, then the time required to cover 1.5 km=60/30 * 3/2 =3 min ... (iii)

∴ Time lost = 4 – 3 = 1 minute Ans.

Click to have hands on MCQs on Kinematics. There are a unit a spread of numerical based mostly queries coated during this

                           
Click to have hands on MCQs on Kinematics . There are a variety of numerical based questions covered in this