Motion In a Straight Line - 11th physics

If an object moving along the straight line and covers equal distance in equal interval of time, it is said to be in Uniform Motion along a straight line.

In Position-Time graph (b) the line shows the uniform motion of the moving object.

Position-Time graph (c) says that object starts moving from origin point O and picks up speed till t = 10s. And thereafter moves with uniform speed till t = 18s. Then brakes are applied and moving object stops at t = 20s. In this case it covers a distance x = 296m.

Speed

Distance covered by a moving object in unit time is called Speed.

Thus speed (v) = Distance covered (s)/Time(t)

Thus, speed can be defined as the distance covered by moving object divided by time taken to cover that distance.

Example:

If a car covers a distance of 50km in 5 hours, then find the speed of the car.

Solution:

Given, distance (s) = 50 km

Time (t) = 5h

Thus, speed (v) = ?

We know that, speed(v) = Distance(s)/Time(t)

Thus, speed (v) =50km/10h = 10km/h

Thus, speed of the given car = 10km/h or 10km h^–1

SI unit of speed

The SI unit of speed is meter per second. Or m/s or ms^–1

Speed has only magnitude and no direction. Thus speed is a scalar quantity.

Average Speed

Average Speed is defined as the Total path length travelled divided by total time interval taken during which the motion has taken place.

Thus, Average Speed = Total Path Length/Total Time Interval

SI Unit of Average Speed

The SI Unit of Average Speed is same as speed. That is the SI Unit of Average Speed is meter per second or m/s or ms^–1.

However in many situations like long distance covered the speed and average speed is measured in km/h or kmh^–1.

Velocity and Average Velocity

The rate of change of position of an object with respect to a frame of reference is called the Velocity.

This means the Total Length of path divided by time is called the Velocity of a moving object.

Thus, Velocity (v) = Total Length of Path(s)/Time(t)

⇒ v = s/t

Velocity of an object is similar to speed and its magnitude is equal to the speed. The only difference between velocity and speed is velocity has magnitude and direction both while speed has only magnitude and no direction.

Thus, velocity is a vector quantity as it has both magnitude and direction.

SI Unit of Velocity

The SI unit of velocity is m/s or ms^–. This is similar to speed.

Average Velocity

The Average Velocity is how fast the position of an moving object changing with time in which direction.

Thus, Average Velocity can be defined as the change in position or displacement (Δx) divided by the time interval (Δt), in which the displacement occurs.

Thus, Average velocity,

Where x¹ and x² are the positions of the object at time t² and t¹, respectively.

Here a bar over the symbol of velocity (v) is used to indicate the average quantity.

SI Unit of Average Velocity

The SI unit of Average Velocity is meter per second, i.e. m/s or ms^–1. However km/h or kmh^–1 is used for measuring the long distance and is generally used in many everyday applications.

Similar to displacement and velocity the Average Velocity is a vector quantity as it has both magnitude and direction.

Positive, Negative and Zero Average Velocity

The Average Velocity can be positive or negative depending upon the sign of the displacement.

If the displacement is positive then the average velocity will be positive. And if the displacement is negative, the the average velocity will be negative.

The Average Velocity is zero if the displacement is zero.

Position-Time Graph for positive, negative and zero velocity

The Position-Time Graph (a) shows positive velocity. The Position-Time Graph (b) shows the negative velocity while the graph (c) shows the zero velocity.

Instantaneous Velocity And Speed

The Velocity of a moving object at particular instants of time interval is called the Instantaneous Velocity.

That is the velocity (v) at an instant (t) is termed as Instantaneous Velocity.

The velocity at an instant is defined as the limit of the average velocity as the time interval Δt becomes infinitesimally small.

In other words,

Where the stands for the operation of taking limit as of the quantity on its right.

In the language of calculus, the quantity on the right hand side of above equation is the differential coefficient of x with respect to t and is denoted by .

The is the rate of change of position of moving object with respect to time at that instant.

Acceleration

The rate of change in velocity of a moving object with time is known as Acceleration.

SI Unit of Acceleration

The SI Unit of Acceleration is m/s/s or ms^–2.

Average Acceleration

The Average Acceleration over a time interval is defined as the change of velocity divided by the time interval.

Where v₂ and v₁ are the instantaneous velocities or simply velocities at time t₂ and t₁. It is the average change of velocity per unit time.

Instantaneous Acceleration

The Instantaneous Acceleration is defined in the same way as the instantaneous velocity.

That is,

The acceleration at an instant is the slope of the tangent to the v–t curve at that instant. Graphically for v–t curve, we can obtain acceleration at every instant of time.

When the acceleration is uniform, obviously, it is equal to the average acceleration over that period.

Since velocity is a quantity having both magnitude and direction, a change in velocity may involve either or both of these factors. Acceleration, therefore, may result from a change in speed (magnitude), a change in direction or change in both.

Positive, Negative or Zero Acceleration

Similar to velocity, acceleration can also be positive, negative or zero.

Position-Time graphs for motion with positive, negative and zero acceleration.