Distance Time Graph For Uniform Motion


 
 
Concept Explanation
 

Distance Time Graph For Uniform Motion

The change in the position of an object with time can be plotted on the distance - time graph by choosing a scale best suited. To draw distance-time graph, time is plotted along X-axis and the distance of the body is plotted along Y-axis.

In this case, the slope of the distance-time graph is equal to the speed of the object.

Distance - Time graph for Uniform Motion

If an object travels equal distances in equal intervals of time, then it moves with uniform speed. For uniform speed, a distance- time graph represents a straight line.

From the graph, it is clear that in equal interval of time 2s, the object covers equal distance 4m, so the motion is uniform and graph is a straight line.

Calculation of speed

To calculate the speed of the object from a distance-time graph, we calculate the slope of the line. The slope is defined as the ratio of change in the value of y with the change in the value of x because the change in y represents the distance and change in x  represents time. Ratio of distance with time represents speed. To find the change in x and y we choose any two points say A and B on the straight line. From points A and B, draw perpendicular AE and BC respectively, on time axis. the difference of the value represented by Point C and E represents a change in time.From points A draw perpendicular AD and BC. The difference of the value of distance at point B  and D represents a change in distance.

The distance traveled by the object from point A to B is = BC - DC = s_2-s_1

Time taken by the object to cover this distance = OC - OE =  t_2-t_1 large therefore speed;(v)=frac{Delta s}{Delta t}=frac{s_2-s_1}{t_2-t_1}=slope;of;distance-time;graph

ILLUSTRATION : The graph below shows the positions of a body at different times. Calculate the speed of the body as it moves from

(i) A to B,                 (ii) B to C and                             (iii) C to D.

SOLUTION: (i) For the motion from point A to B,

time taken, t= 4 -1 = 3 s             Distance covered = 8 - 2 = 6 m

Speed; during ;the ;motion; from ;point ;A;to;B=frac{Distance}{Time}=frac{6}{3}=2m/s

 (ii) For the motion from point B to C,

time taken , t = 7 - 4 = 3 s                    Distance covered = 8 - 8 = 0 m

Speed; during ;the ;motion; from ;point ;B;to;C=frac{Distance}{Time}=frac{0}{3}=0m/s

(iii) For the motion from point C to D,

time taken, t = 10 - 7 = 3 s                 Distance covered = 17 - 8 = 9 m

Speed; during ;the ;motion; from ;point ;C;to;D=frac{Distance}{Time}=frac{9}{3}=3m/s

 
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