What is the nature of velocity-time graph for a body moving with uniform acceleration when initial the body is at rest?

Answer

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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.