One dimension implies motion along a straight line or in a single direction. Consider a car or a person driving down a straight road or jogging on a straight track. Think of an object being tossed vertically into the air and then watching it fall. These are examples of one-dimensional motion. There are four main factors to keep track of when evaluating the motion of objects. Time, displacement, velocity, and acceleration are the four variables; time is a scalar quantity, and the other three are vector quantities.
Table of Contents
- Distance and Displacement
- Speed and Velocity
- Acceleration
- Kinematic Equations when Acceleration Is Constant
- Frequently Asked Questions
Distance and Displacement
Distance travelled, or path length is the actual distance covered by the moving object in a given interval of time. It is a scalar quantity.
The change in the position of the object along a particular direction is called displacement.
Displacement Ξx = xf – x0
xf is the final position of the object.
x0 is the initial position of the object.
The difference between your ending position (xf) and your beginning point (xo) is known as displacement.
Displacement is a vector quantity. This means it has direction and magnitude, and it is visually depicted as an arrow pointing from the starting point to the ending location. Your displacement is 5 metres north if you start in a specific location and then move north 5 metres from where you started. Then, if you turn around and return with a 5 m south displacement, you will have travelled a total distance of 10 m, but your net displacement will be zero because you are back where you began.
Speed and Velocity
The time rate of change of the position of the particle is called speed. Speed tells about how fast or how slow the particle is moving. It gives the distance covered by the particle in unit time. Speed is a scalar quantity, and its SI unit is m/s. The speed of the object will never be negative; it will either be positive or zero.
The time rate of change of position of an object in a particular direction is called velocity. Velocity can be defined as the time rate of change of displacement. Also, speed in a particular direction can be called velocity. Velocity is a vector quantity with both direction and magnitude. The unit of velocity is m/s. The value of velocity can be positive, negative or zero.
Average Speed and Average Velocity
The average speed of motion of a particle is defined as the ratio of the time travelled to the elapsed time.
Average speed = total path length/total time taken
Average velocity is defined as the total displacement by the body in time t.
Average velocity = total displacement/total time
Vavg = (Ξx/Ξt) = (xf – x0)/(tf – t0)
Vavg = average velocity
Ξx = change in position
Ξt = change in time
xf and x0 are the beginning and ending positions at time tf and t0, respectively.
Instantaneous Velocity
If we consider an infinitesimally small time interval, we get more detailed information. The average velocity becomes the instantaneous velocity for an infinitesimally small interval of time or the velocity at a single moment over such a time range. A car’s speedometer displays the instantaneous speed. However, for calculating the time taken to travel from one point to another, average velocity is needed. The average velocity at a specific point in time or across an infinitesimally brief time interval is called instantaneous velocity. The instantaneous velocity can be found by taking limits.
Uniform Velocity
A body is said to be moving with uniform velocity if equal changes of displacement take place in equal intervals of time, however small these intervals of time may be. When the body moves with uniform velocity, neither the magnitude nor the direction of velocity changes.
Acceleration
Any process in which the velocity varies is referred to as acceleration. As velocity involves both speed and direction, a body gets accelerated when there is a change in speed, direction or both. If there is no change in the speed or direction of the object, there will not be any acceleration, no matter how quickly the object moves. A jet moving at 800 miles per hour along a straight line has zero acceleration, despite the fact that it is moving very quickly. It will have acceleration while it lands because the jet is slowing down.
Average acceleration is defined as the rate of change of velocity with time.
a = (Ξv/Ξt)= (vf – vi)/Ξt
vi = initial velocity
vf = final velocity
Ξt = time
The SI unit of acceleration is m/s2.
The instantaneous acceleration is
Uniform or Constant Acceleration
A body is said to be moving with uniform or constant acceleration if its velocity changes by equal amounts in equal intervals of time, however small these time intervals may be. When the body moves with constant acceleration, the average and instantaneous acceleration of the body are equal.
Kinematics Equation when the Acceleration Is Constant
A particle moving along a straight line with constant acceleration is said to execute uniformly accelerated motion in one dimension. This type of motion is the simplest kind of accelerated motion. The velocity of the particle changes at the same rate throughout the motion. Some simple equations which relate displacement (S), initial velocity (u), final velocity (v), time taken (t), and uniform acceleration (a) can be obtained, and these equations are called kinetic equations for the one-dimensional motion of the particle. The equations are as follows:
1. v = u + at
v = final velocity
u = initial velocity
a = uniform acceleration
t = time taken
2. S = ut + (Β½)at2
S = displacement
u = initial velocity
t = time taken
a = uniform acceleration
3. v2 = u2 + 2aS
v = final velocity
u = initial velocity
a = uniform acceleration
S = displacement
4. Sn = u + (a/2)(2n – 1)
Sn = displacement in the nth second of motion.
5. a = (S2 – S1)/n2
S2 and S1 are the displacements in two consecutive equal intervals of time βnβ.
Motion in One Dimension – Video Lessons
L1 – Introduction to Kinematics
L2 – Equations of Motion
L3 – Motion Under Gravity
L4 – All Important Graphs in One Shot
Motion in One Dimension – JEE Revision
Frequently Asked Questions on Motion in One Dimension
Can the speed of the body change if its velocity is constant?
If the velocity of a body is constant, it means that the magnitude and direction of the velocity do not change. Since the magnitude of the velocity is speed, the speed of the body cannot change.
Define one-dimensional motion.
The motion of a body is a one-dimensional motion if it moves along a straight line.
Define the displacement of a particle.
The change in the position of a particle along a particular direction over a given period of time is called the displacement of the particle.
Define acceleration.
The rate of change of velocity of an object is known as the acceleration of the object.
Write the SI unit of acceleration.
The SI unit of acceleration is m/s2.
Does the average velocity over any interval of time differ from the instantaneous velocity when the velocity is constant?
No, average velocity over an interval of time is equal to the instantaneous velocity, provided the velocity of a body is uniform or constant.
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