# Graphical representation of motion

Question 1 What is the nature of graph for a uniform speed?

Question 2 Name the quantity which is measured by the area occupied under the velocity-time graph?

Question 3 What does the slope of speed-time graph indicate?

Question 4 What can you say about the motion of a body if its displacement-time graph is a straight line?

Question 5 What can you say about the motion of a body if its velocity-time graph is a straight line?

Question 6 Name the quantity,the slope of whose graph give Speed?

**Graphical representation of motion**

**Distance – Time graphs**

**
**1)

**Uniform speed**

Straight line graph between distance and time tells us that body is moving with uniform speed.

Slope of distance time graph indicates speed.

PQ

Slope = ———

OQ

2)**Non-Uniform speed**

The distance time graph for a non-uniform motion is a curved line(parabola).

If a body moves with a non-uniform speed then its motion is said to be accelerated.It also represents distance time graph with accelerated motion.

**Speed – Time or velocity – time graphs**

**
**1)

**Speed-time graph when speed remains constant**

a)Speed time graph for a body moving with constant speed(no acceleration) is a straight line parallel to time axis.

We can find the distance travelled by a body in a given time from speed-time graph.

Distance travelled

Speed =—————————-

Time Taken

OC * BC = Distance travelled

OC * OA = Time taken

Distance travelled = Area of rectangle OABC

The velocity time graph of an object moving with constant velocity is a straight line parallel to time axis.

2)**Speed-time graph when speed changes at uniform rate(uniform acceleration)**

1)When a body moves with uniform acceleration,its speed changes by equal amount in equal intervals of time.

Speed time graph for a uniformly changing speed will be a straight line.

The value of acceleration from speed time graph of moving body can be calculated as:

Change in speed or velocity

a = ————————————-

Time taken

PQ

a=——–

OQ

In a speed time graph the acceleration is given by slope of the graph.

The distance travelled by a moving body in a given time can be calculated from speed time graph.

Distance travelled = Area of triangle POQ

= 1

—- * OQ * OP

2

In a speed time graph of a body a straight line sloping downwards indicates retardation.

**Speed time graph when the initial speed of the body is not zero**.

The distance travelled by the body in this case is equal to the area of trapezium OBCA.

Sum of parallel sides * Height

Area of Trapezium=————————————–

2

(OB * AC) * OA

Distance Travelled = —————————

2

**3)Speed -Time graph when speed changes at a non-uniform rate(Non-uniform acceleration)**

**
**When the speed of a body changes in an irregular manner,then speed-time graph of a body is curved line.

nice graphs help me a lot….

yes khushi you are right it is very helpful