Kinematics Or Motion In A Straight Line

Displacement-time graphs:These graphs are down by ploting displacement on Y-axis and time on X-axis .Slope of this graph gives velocity

a)If the graph is a straight line parallel to time axis,then body is at rest.Body has some intial displacement \( S_0 \)
b)If the graph is a straight line with a positive slope,then the body is moving with constant velocity.Graph(1) represents that body has zero initial displacement and graph(2) represents that body has intial displacement \( S_0 \) .
    
                            
c)If the graph is a parabola or with a slope which increases at a steady rate,then body is moving with uniform acceleration.In case (1) body has no intial displacement and in case (2) body has  intial displacement \( S_0 \)
           
                                                                                                                                               
d) If the graph is a parabola or with a slope which decreases at a steady rate,then body is moving with uniform retardation.
           

e)For a body projected vertically up,this graph is a parabola as shown
        

f)If  the graph is a straight line with negative slope as shown,than body is approaching the observer with  constant velocity.
         

g)These two graphs are impossible
        

VELOCITY-TIME GRAPHS
This graph is plotted by taking velocity on Y-axis and displacement on X-axis slope of this graph represents acceleration.Area under this graph gives displacement
a)If the graph is a straight line parallel to time axis, then body is moving with uniform velocity ‘u’.
                

b)If the graph is a straight line with a constant positive slope,then body is moving with uniform acceleration.
1)represent that body started from rest.
2)represent that body has initial velocity ‘u’.

c)If the graph is a straight line with a constant negative slope,then body is moving with uniform acceleration.
                       

d)If the graph is a parabola or with a slopewhich increases at a steady rate,body is moving with increasing acceleration.
      

e)For a body projected vertically upwards from the ground,graph will be as shown.
Here \( t_1 = \frac{u} {g};t_2 = \frac{{2u}} {g} \)  
   

Area below the graph is zero.Which indicates zero displacement on reaching ground.
f)For a body projected vertically up from the top of a tower,graph will be as shown.Area below the  graph gives -h where h is tower height.


g)If a body is released from certain height and which undergoes elastic collision with the floor,velocity time graph will be as shown
            
   
h)If the body undergoes inelastic collision with the floor,then graph will be as given below.After sometime,body will stop.
          
     
i)If the body starts from rest and moves with uniform acceleration for some time and then moves with uniform retardation until it stops.(shape is triangle)
             

j)If the body starts from rest,and moves with uniform acceleration for some time,and then moves with uniform retardation until it stops.(shape is trapezium)
 

k)A body moved with uniform velocity for some time,and then moves with uniform retardation until it stops.
   

ACCELERATION-TIME GRAPHS
This graph is drown by plotting acceleration on Y-axis and time on X-axis .Area below the graph gives change in velocity.
a)For a body moving with uniform acceleration,graph is a straight line parallel to time axis
b)For a body moving with an acceleration which increases at a steady rate,it will be a straight line with a positive slope.