# Quantities of physics in the linear motion

**1. Time interval**

When an object moves from one place to another, the object needs a certain time interval. The time symbol is t (time). The international system unit of time is second (s).

**2. Distance and displacement**

Distance is the length of the path taken by an object. Distance is a scalar quantity, where the quantity does not depend on direction. The distance symbol is d and the international system unit is a meter (m).

Displacement is a change in the position of an object. Displacement is vector quantities, so displacement consists of the magnitude of displacement and direction of displacement. The displacement depends on the direction so that it can be positive or negative. If it is figured in Cartesian coordinates then according to the agreement, if the direction of displacement is in the direction of the positive x-axis and the positive y-axis, then the displacement is positive. On the contrary, if the direction of displacement is in the direction of the negative x-axis and the negative y-axis then the displacement is negative. The direction of displacement is also commonly stated in the north, east, south, west. The symbol of displacement is d and the international system unit is a meter (m).

Sample problem 1 :

A student moves east as far as 2 meters. What are the distance and the magnitude of the displacement of the student?

a = initial position, b = end position.

Distance (d) = 2 m

The magnitude of displacement (d) = 2 m. Direction of displacement = east

Sample problem 2 :

A student moves east as far as 2 meters and then moves west as far as 2 meters. What is the distance and magnitude of the displacement of the student?

a = starting position and final position

Distance (d) = 2 m + 2 m = 4 m

The magnitude of displacement (d) = 2 m – 2 m = 0. End position = initial position so that there is no displacement.

Sample problem 3 :

A student moves east as far as 2 meters and then moves west as far as 1 meter. What is the distance and magnitude of the displacement of the student?

a = starting position, b = end position.

Distance (d) = 2 m + 1 m = 3 m

The magnitude of displacement (d) = 2 m – 1 m = 1 m. Direction of displacement = east

**3. Speed and velocity**

Speed is a scalar quantity, while velocity is a vector quantity. Velocity consists of a magnitude of velocity and direction of velocity. The symbol of velocity is v and the symbol of velocity is v (velocity). The international system unit of speed and velocity is meter per second (m/s).

**a. Average speed and average velocity**

Sample problem 1 :

A student moves east as far as 2 meters for 1 second. What are the average speed and the magnitude of the average velocity of the student?

The direction of the average velocity = direction of displacement = to east

Sample problem 2 :

A student moves east as far as 2 meters for 1 second and then moves west as far as 1 meter for 2 seconds. What are the average speed and the magnitude of the average velocity of the student?

Direction of average velocity = direction of displacement = to east

**b. Instantaneous speed and instantaneous velocity**

Instantaneous speed = very small distance traveled during a very short time interval. The magnitude of the instantaneous velocity = very small displacement traveled during a very short time interval. If you have ever ridden a motorcycle or car, you certainly have seen a speedometer. When riding a motorcycle, the speed of a motorcycle changes and shown by the speedometer.

In physics, instantaneous speed is often abbreviated as speed. Likewise, the instantaneous velocity is often abbreviated as velocity. Please note that we can replace the magnitude of the velocity with speed. This is because the magnitude of velocity is considered equal to speed. The magnitude of velocity is considered equal to speed because distance and the magnitude of displacement are the same if it is very small. Although the distance and the magnitude of the displacement are not always the same (compare with the discussion about distance and displacement), but if the distance and the magnitude of the displacement are very small then they must have the same value.

**4. Acceleration**

Acceleration is a vector quantity so there is the magnitude of acceleration and direction of acceleration. The symbol of acceleration is a (acceleration). SI unit of acceleration is meter per second squared (m/s^{2}).

**a. Average acceleration**

Sample problem :

A car starts moving east from rest until it reaches a speed of 10 m/s for 5 seconds. Calculate the magnitude of the average acceleration!

The direction of the average acceleration to the east.

On average, the speed of the car increases by 2 m/s every second. If the magnitude of the acceleration of the car is constant then the speed of the car always increases by 2 m/s every second. If the magnitude of the acceleration of the car is not constant then the speed of the car does not always increase by 2 m/s every second. May the speed of the car increase by 1 m/s at the first second, then increases by 3 m/s in the second. But on average, when moving for 5 seconds, the magnitude of the velocity of the car increases by 2 m/s every second.

**b. Instantaneous acceleration**

Instantaneous acceleration is a change in velocity during a very short time interval. Instantaneous acceleration is often called acceleration. Therefore if it is said to be acceleration, what is meant is instantaneous acceleration. An object is said to experience acceleration if its velocity changes. Velocity is also a vector quantity, which includes the magnitude of the velocity and the direction of velocity. Therefore there are three conditions in which a moving object is said to be accelerating. First, an object is said to experience acceleration if the magnitude of velocity or speed changes (the direction of velocity is constant).

In the first example, a car is initially at rest (v = 0). One second later its speed increases to 5 m/s. The speed of the car increases so the car is said to be accelerating. In the second example, a car initially moves at a speed of 5 m/s. One second then the car stops. The speed of the car decreases because the car is said to experience a negative acceleration or the car experiences a deceleration. Second, an object is said to experience acceleration if the direction of its velocity changes (the magnitude of velocity or speed is constant). Direction of velocity = direction of displacement = direction of movement. Third, an object is said to experience acceleration if both the magnitude and direction of its velocity change.