Question

What would be acceleration of a body if its velocity-time graph
is a line parallel to the time axis?​

Answer 1

GiveN :-

• In a velocity time graph the line is parallel to the x axis .

To FinD :-

• The nature of acceleration of the body.

SolutioN :-

Here it's given that in a velocity time graph the line is parallel to the x axis . This means that the velocity of a body is constant and its not increasing . This implies that the acceleration of the body is zero . Since the velocity is not increasing hence the acceleration of the body will be zero .

$\underline{\textsf{\textbf{\pink{ Graph will be as below :- }}}}$

$\setlength{\unitlength}{1 cm}\begin{picture}(12,8)\thicklines\put(0,0){\vector(1,0){5}}\put(0,0.01){\vector(0,1){5}} \put(0,2){\line(1,0){5}}\put(2,-0.5){\sf Time \longrightarrow } \put(-1.5,2.5){\sf Velocity \uparrow } \end{picture}$

This can be proved also . We know that the slope of velocity time graph gives acceleration . Since the graph is a straight line hence it's perpendicular will be zero . And we know that the slope is $\tan\theta$

$\sf:\implies \pink{ Slope = tan\theta }\\\\\sf:\implies Slope = \dfrac{perpendicular}{base}\\\\\sf:\implies Slope =\dfrac{0}{Base}\\\\\sf:\implies\underset{\pink{\sf Hence \ Proved }}{\underbrace{\boxed{\pink{\frak{ Acceleration = 0 }}}}}$