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Distance-Time Graph

Distance-time graph plays a key role during the calculation of various values associated with motion in physics. This graph can be used in mechanics as well. Using this graph, it is very easy to compare two journeys that are happening in a simultaneous manner.

In general, it is nothing but a line graph that helps us derive various concepts such as velocity, speed, and acceleration, etc. These are not just some random concepts in physics but they also act as a foundation for applied physics which are very useful while solving real-life problems.

Definition of Distance vs Time graph

The three most important elements which can be discussed while learning about the distance-time graph are time, speed, and distance. In a graphical representation, time is on the bottom X-axis whereas distance is placed on the vertical Y-axis. From this, one can easily plot the values in the graph once they are done determining the axes.

This distance vs time graph teaches us about the different variations of movement of a body. To give an example, when the graph plots form a straight line, it indicates that the body moves at a fixed (or constant) speed. The following graph is the illustration of the same -

Time Graph

Examples and description of distance vs time graph

Look at the following graphs and try to observe the nature of movement of the body -

Time Graph

In the first figure, we can clearly see that the curve line presented in the distance vs time graph moves upwards. This indicates an increase in terms of speed, which can also be termed acceleration.

Meanwhile, in the second picture, the curve bends towards the down direction. This denotes that the speed of the body is decreasing. In simple words, this downgrade indicates the deceleration of the object. In both, calculation of speed can be easily done in the following two ways: First, draw a tangent with respect to the curve, and then measure the gradient of the tangent.

In order to calculate the speed of the object, we can also use the below-mentioned formula,

Speed=change in distance/change in time

Apart from that, one needs to remember that the velocity and vector quantity of the object changes with respect to magnitude and direction. These are important concepts to learn while studying circular motion.

Distance vs Time graph worksheet

In order to understand the topic even better, one needs to work out some critical problems related to this concept. So, given below are some of the basic problems to help students understand the concept of distance vs time graph,

Problem 1:

John is a construction worker who travels to work every day. Using the following data given in the graph, find the following:
1. Total distance covered by John
2. His rest time
3. The average speed between the timings 5:15 PM and 5:45 PM (in terms of kilometers)

Solution:

  • At first, John had travelled a distance of 25 km from the axis and then taken a rest followed by going back home. So, the total distance travelled by John is 25 km + 25 km which gives 50 km.
  • From the graph, we can vividly see that John made no movement for a specific duration which covered one box in the graph. Meanwhile, we can witness that the two total boxes can be equal to 15 mins from the axis. Hence, the stationary time of John is 15/2 which is equal to 7.5 mins
  • Lastly, in order to find the average speed between the places, we need to define the gradient of the graph first. To define the gradient, we should take into consideration from 5:15 PM to 5.45 PM, which can be 30 mins (or 0.5 hours). Hence, John travelled a total of 20 km between this timing and the gradient can be equal to 20/0.5, which gives 40 km/h.

Conclusion

  • Motion is considered uniform if the distance vs time graph plot forms a straight line.
  • The speed of any body or object can be easily calculated with the help of a slope drawn in the distance vs time graph
  • The slope drawn from the straight line graph can be seen as the same irrespective of the interval which has been chosen. This can clearly state that the speed of that particular object or body is found to be remaining at a constant value during uniform motion.

 

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