- Graphical Representation of Motion:
The change in the position of an object with time can be represented on the distance-time graph. In this graph, time is taken along the x–axis and distance is taken along the y-axis.
Distance-time graphs can be employed under various conditions where objects move with uniform speed, non-uniform speed, remain at rest etc.
When an object travels equal distances in equal intervals of time, it moves with uniform speed. This shows that the distance travelled by the object is directly proportional to time taken. Thus, for uniform speed, a graph of distance travelled against time is a straight line whereas for non-uniform speed it is a curved line.
The variation in velocity with time for an object moving in a straight line can be represented by a velocity-time graph. In this graph, time is represented along the x-axis and the velocity is represented along the y-axis. If the object moves at uniform velocity, the height of its velocity-time graph will not change with time. It will be a straight line parallel to the x-axis. To determine the distance moved by the car from its velocity-time graph, the area under the velocity-time graph gives the distance (magnitude of displacement) moved by the car in a given interval of time.
For example, if the car would have been moving with uniform velocity, the distance travelled by it would be represented by the area ABCD under the graph. Since the magnitude of the velocity of the car is changing due to acceleration, the distance s travelled by the car will be given by the area ABCDE under the velocity-time graph.
That is,
s = area ABCDE = area of the rectangle ABCD + area of the triangle ADE
= AB × BC + 1/2 (AD × DE)
In the case of non-uniformly accelerated motion, velocity-time graphs can have any shape.
- Equations of Motion by Graphical Method:
When an object moves along a straight line with uniform acceleration, acceleration during motion and the distance covered by it in a certain time interval by a set of equations known as the equations of motion. Three equations of motion:
i. v = u + at
ii. s = ut + ½ at2
iii. 2as = v2 – u2
where u is the initial velocity of the object which moves with uniform acceleration a for time t, v is the final velocity, and s is the distance travelled by the object in time t.
Meghna Thapar 4 years, 4 months ago
The change in the position of an object with time can be represented on the distance-time graph. In this graph, time is taken along the x–axis and distance is taken along the y-axis.
Distance-time graphs can be employed under various conditions where objects move with uniform speed, non-uniform speed, remain at rest etc.
When an object travels equal distances in equal intervals of time, it moves with uniform speed. This shows that the distance travelled by the object is directly proportional to time taken. Thus, for uniform speed, a graph of distance travelled against time is a straight line whereas for non-uniform speed it is a curved line.
The variation in velocity with time for an object moving in a straight line can be represented by a velocity-time graph. In this graph, time is represented along the x-axis and the velocity is represented along the y-axis. If the object moves at uniform velocity, the height of its velocity-time graph will not change with time. It will be a straight line parallel to the x-axis. To determine the distance moved by the car from its velocity-time graph, the area under the velocity-time graph gives the distance (magnitude of displacement) moved by the car in a given interval of time.
For example, if the car would have been moving with uniform velocity, the distance travelled by it would be represented by the area ABCD under the graph. Since the magnitude of the velocity of the car is changing due to acceleration, the distance s travelled by the car will be given by the area ABCDE under the velocity-time graph.
That is,
s = area ABCDE = area of the rectangle ABCD + area of the triangle ADE
= AB × BC + 1/2 (AD × DE)
In the case of non-uniformly accelerated motion, velocity-time graphs can have any shape.
When an object moves along a straight line with uniform acceleration, acceleration during motion and the distance covered by it in a certain time interval by a set of equations known as the equations of motion. Three equations of motion:
i. v = u + at
ii. s = ut + ½ at2
iii. 2as = v2 – u2
where u is the initial velocity of the object which moves with uniform acceleration a for time t, v is the final velocity, and s is the distance travelled by the object in time t.
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