What is the nature of velocity-time graph of a body moving with uniform acceleration?

1. Describing Motion:

(i) When a body does not change its position with respect to time and a reference point, it is said to be at rest with respect to that reference point.

(ii) When the position of a body continuously changes with respect to the time and a reference point it is said to be in a state of motion.

(iii) Distance is the actual length of the path travelled by a moving body, irrespective of the direction in which the body moves. It is a scalar quantity.

(iv) Displacement is the shortest distance covered by a moving body from the point of reference in a specified direction.

(v) A body is said to be in uniform motion if it covers equal distance in equal intervals of time. 

(vi) A body is said to be in non-uniform motion if it covers unequal distances in equal intervals of time.

2. Rate of Motion:

(i) Speed is the distance travelled by a body in unit time. It is a scalar quantity and its SI unit is m/s.

(ii) Velocity is the displacement covered by a body in a unit time in a specified direction. It is a vector quantity and its SI unit is m/s.

3. Acceleration and Retardation:

(i) Acceleration is the rate of change of velocity. Its SI unit is m/s2.

(ii) Negative acceleration is called retardation. The velocity of a retarding body decreases with time.

4. Graphical Representation of Motion:

(i) The change in the position of an object with time can be represented on the distance-time graph adopting a convenient scale of choice.

(ii) The slope of distance-time graphs gives the speed.

(iii) The variation in velocity with time for an object moving in a straight line can be represented by a velocity-time graph.

(iv) The slope of a velocity-time graph gives acceleration.

(v) The area under the velocity-time graph gives the displacement. 

5. Equations of Motion:

(i) First equation of motion: v=u+at

(ii) Second equation of motion: s=ut+12at2

(iii) Third equation of motion: v2-u2=2as
Where u is the initial velocity, v is the final velocity; s is the distance covered, t is the time taken and a is the acceleration of the moving body.

6. Uniform circular motion:

(i) If an object moves in a circular path with uniform speed, its motion is called uniform circular motion. 

(ii) Uniform circular motion is an accelerated motion.

Equations of motion help us solve numerous problems and predictions related to motion. Let us understand their derivation using graphs in this video.

Graphs are a visual representation of information. In this video, we will learn how to draw a graph and how to use it with the help of examples.

The centripetal acceleration is responsible for keeping an object performing circular motion in a circular path. This video derives an expression for centrip...

You see stationary and moving objects all around you. But are the stationary objects really at rest? Watch this video and learn about the different motion ar...

Did you know that centrifugal force isn't really a thing? I mean, it's a thing, it's just not real. In fact, physicists call it a "fictitious force." Learn w...

Do you want to understand the concept of circular motion? Watch this video and learn why the instantaneous velocity of an object moving in a uniform circular...

Answer

Verified

Hint: Velocity-time graph of an object moving with uniform acceleration. When the velocity – time graph is plotted for an object moving with uniform acceleration, the slope of the graph is a straight line, the pattern of slope of the graph shows that object is moving with uniform acceleration.

Complete step by step answer:

In the sequence,$S$ is displacement,$u$ is initial velocity,$t$ is time,$a$ is acceleration$V$is final velocity ${V_{av}}$angle velocityFrom that,$av$ velocity ${v_{av}} = \dfrac{{u + v}}{2}$. . . (1)${V_{av}} = \dfrac{S}{t}$. . . (2)From (1)$\dfrac{s}{t} = \dfrac{{u + v}}{2}$ multiply$ \to S = \dfrac{{\left( {u + v} \right)t}}{2}$. . . (3)From (2) equation of motion$v = u + at$. . . (4)Resulting value of (4) and (3)$S = \dfrac{{(u + u + at)t}}{2}$$ \Rightarrow S = \dfrac{{ut + ut + a{t^2}}}{2}$ by separating the equation,$  S = \dfrac{{2at}}{2} + \dfrac{{a{t^2}}}{2} \\\implies S = ut + \dfrac{1}{2}a{t^2} \\ $

Additional Information:

Advantage of speed time graph speed-time graphs are very useful when describing the movement of an object. This is a velocity time graph of an object moving in a straight line due to North. The displacement of this object is the area of the velocity time graph. A sloping line on a speed-time graph represents acceleration.

Note:

if an object's speed is increasing at a constant rate then we say it has uniform acceleration; the rate of acceleration is constant. If a car speeds up, then slows down then speeds up doesn’t have uniform acceleration. Non-uniform means that the acceleration is not uniform. Uniform acceleration is change of equal velocity in equal intervals of time. Non-uniform acceleration is change of non-equal velocity in equal intervals of time.