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Speed Time Graphs - Physics

Speed

Speed, in general terms, is defined as the rate of change of the distance covered by an object in unit time. Since speed only refers to the magnitude and not the direction, it is a scalar quantity. Speed is given by the formula s=d/t where s is the speed, d is the distance covered by the object, and t is the time taken by the object to cover that distance. m/s (meter per second) is the SI unit of speed but km/h (kilometre per hour) is the commonly used unit of speed throughout the world, except in the USA and the UK, where the preferred unit for speed is mph (miles per hour).

  • Instantaneous Speed: The measured speed of an object in motion either at one particular instant or for a short span of time is called instantaneous speed. It is given by v=ds/dt, where v is the instantaneous speed, and ds/dt is the rate of change of distance/position at a specific instant.
  • Average Speed: Unlike instantaneous speed, average speed gives us the value of speed for the entire duration of the whole time interval. Suppose, for example; a vehicle covers 500 kilometers in 10 hours. In that case, the average value is calculated using the formula v=s/t to be 50 km/h. However, it is very unlikely that the vehicle maintained a constant velocity of 50 km/h throughout its 10-hour journey.
  • Tangential Speed: It is the speed possessed by an object having a circular path of motion. It is given by v=ωr where v is the tangential speed, ω is the rotational speed, and r is the radial distance. The rotational speed is less near the center and goes up in value as we move away from the center.

Speed Time Graphs

Speed time graphs are an extremely handy tool as it helps us to define the motion of an object for any given interval of time. Acceleration of the object, average speed and instantaneous speed of the object at any instant of time, total distance covered, total time taken by the body to cover that distance and whether or not the body was in motion at a specific time are some of the data that can be derived from a speed-time graph. The speed of the object is plotted along the y axis, and the time taken by the object is plotted on the x-axis of the graph. The distance covered is given by the area under the speed-time graph. When the values of speed with respect to time are plotted on the graph, and we get a sloping line, that means the object has positive acceleration, and that slope gives us the value of acceleration. The greater the slope’s angle is with respect to the x axis, the greater is the value of acceleration. But if the slope is downwards from right to left, then that means the object has decelerated at that interval of time. But throughout the graph, if there are no slopes, the object is said to have had a constant velocity.

Acceleration

The rate of change of velocity with respect to time is called acceleration. It is a vector quantity because both magnitude and direction has to be considered when measuring acceleration. Its unit is ms-2 (meter per square second).

Types of Speed Time Graphs

Let us discuss the different types/cases of speed-time graphs with the example below.

Properties of the reflection of waves

Certain properties of the reflection of waves are mentioned below:

  1. Constant Acceleration (increasing speed)

    In sections A, C of the graph, we can see that the graph rises steadily and has a slope. This means that the body in motion constantly increased its speed with respect to time at these parts of its motion. Therefore, the body is said to have accelerated. The speed in the A section of the graph is given by

                   v = u + at

    Since the body starts from rest, the initial velocity u=0. So the equation becomes

                   v=at

  2. Zero Acceleration (constant speed)

    In section B, there is no slope, and the graph is rather a straight line. This means that the body in motion did not accelerate and maintained a constant speed throughout that interval of time. Since acceleration a=0

                   v = u

    That is, the initial speed and average speed are the same.

  3. Negative Acceleration (deceleration)

    In section D, the graph slopes down from right to left. This is because the body slowed down with time (i.e.) it decelerated till it eventually came to a position of rest where its speed is zero. Here, the speed is given by

                   v = u – at

    This is because deceleration, like acceleration, is a vector quantity, and the direction is considered too.

Various Types of Waves

There are many types of waves that exist. Some of them are mentioned briefly below:

  • Longitudinal waves- These kinds of waves propagate in the same medium and in the same direction as that of the incident waves. The propagation of these waves includes alternate compressions and rarefactions. These waves can travel in solids as well as liquids.
  • Transverse waves- These kinds of waves propagate in the perpendicular direction to that of the incident waves. These waves propagate by forming alternate crests and troughs. These waves can only travel through a solid medium.
  • Electromagnetic waves- These waves are formed by the periodic and uniform, mutually perpendicular electric and magnetic fields, which are normal to the plane of the propagated wave. These behave like transverse waves, but unlike them, they can also travel in a vacuum and not just through solids. Light is an example of these types of waves.
  • Reflection at an open boundary- When an incident wave is struck at an interface with an open end, then the wave undergoes partial refraction and reflection.
  • Reflection at a closed boundary- When an incident wave is struck at an interface with a closed-end, then the wave undergoes only pure reflection.

Important Points of Reflection

Important points of reflection at a rigid or a closed boundary:

  • Let us consider a string or a rope fixed at one end of the wall, and the other is kept loose.
  • Now, when an incident wave or a pulse is generated from the free end of the wave, a force is acted on the wall.
  • Because of Newton's third law of motion, the wall also exerts a force equal in magnitude and opposite in direction. The wall on the string exerts this force.
  • Since the wall is a rigid body, it cannot exert the force back, making the attached string generate a pulse of the same magnitude in the opposite direction.
  • In such a case, the phase difference between the two waves is 180 degrees.

Important points of reflection at a free boundary:

  • In this case, the string or the rope is tied to a ring since it has an open end to it.
  • Here, when the initial pulse strikes, the ring moves up and stretches the string. This makes the string produce a reflected pulse with the same sign and amplitude as that of the incident pulse.
  • This results in creating a maximum displacement at the end of the string or the rope.
  • There is no additional phase shift which is why the phase difference between the two waves is zero.

Reflection of waves has a great variety of usage in today's world, and there are many useful applications. Therefore, it is of great importance to learn about this branch of physics.

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