# Acceleration types, units, importance and Graphic representation of moving in a straight line

**When the driver of a moving car uses the brakes, we describe the car movement as a decelerating motion be****cause the car speed decreases as time passes. ****The ratio d/t remains constant in the case of a body that moves at a uniform speed ****because this body covers equal distances at equal periods of time. The body which moves at acceleration can’t move at a regular speed because its speed changes by passing time.
**

### Graphic representation of moving in a straight line

**Graphs and tables are important to physicists, ****Physical phenomena can be described and understood in many ways, ****Physicists use mathematical relations between variables to describe certain phenomena. ****Physicists use other mathematical relations like graphs and tables in order to:**

**predict the relation between certain physical quantities.****understand practical results.****describe the physical phenomena in an easier way.**

#### Graphic representation of regular (uniform) speed

**Facts about regular speed in a straight line:**

**The (distance – time) graph of a regular motion at a constant (uniform) speed is represented by a straight line passing through the origin point because the distance is directly proportional to the time, when the object moves at a constant speed.**

**The (speed-time) graph of a regular motion at a constant (uniform) speed is represented by a straight line parallel to the time axis.**

**The (distance- times) graph of an object at rest is represented by a straight line parallel to the time axis. ****The relation (distance- time) graph for an object that moves at a non-uniform speed is represented as a curved line passing by the origin point.**

### Acceleration

**When you sit in a car next to the driver and the car starts moving from rest in a straight line, you notice that the car speed increases gradually as time passes. ****When the speed of the car at 1 second becomes 5 m/sec., at 2 seconds becomes 10 m/sec., at 3 seconds becomes 15 m/sec. and so on.**

**To describe the change in the car speed in one second in this case, we use a physical quantity called “acceleration“. ****Acceleration is the change of an object speed in one second in a specific direction, or it is the rate of change of speed.**

**Acceleration (a) = Change in speed (ΔV)/Time in which the change occurs (Δt)
**

**Acceleration (a) = [Final speed (V _{2}) − Initial speed (V_{1})]/ Time (Δt)**

**Delta (Δ) means the rate of change of any physical quantity.**

**To calculate V _{1} or V₂: **

**V**

_{1}= V_{2}− (a × t) , V_{2}= V_{1}+ (a × t)#### Measuring units of acceleration

**Acceleration unit = ****metre/second². ****We use the acceleration unit (m/sec².) when the speed is measured in metre/second and the time is measured in second, or (km/h²) when the speed is measured in kilometre/hour and the time is measured in hour.**

#### Guidelines to solve problems on acceleration:

**To calculate: Acceleration, Change in speed, and Time, a = ΔV/ Δt****If the body is moving at a regular speed, so its acceleration equals zero because its speed doesn’t change as time passes [when (AV) = Zero, then (a) = Zero].****If the body starts moving from rest, so its initial speed (V₁) equals zero.****When the body stops moving, so its final speed (V₂) equals zero.****When the car is moving, then the brake is applied to stop the car after a period of time, so, its****final speed equals zero.**

### Uniform acceleration

**When a car covers equal distances at equal periods of time, it is said that the car moves at ****a uniform (regular) speed. ****But if its speed changes (decreases or increases) by equal values at equal periods of time, ****it is said that the car moves at a uniform (regular) acceleration.**

**When t****he speed of the car increases by 10 m/sec each 2 sec, so, Acceleration (a) = (20- 10)/ 10 = 5 m/sec². ****Uniform acceleration ****is an acceleration by which an object moves in a straight line when its speed changes by equal values through equal periods of time.
**

**When a car moves at a uniform acceleration equals 5 m/sec². This means that the car moves in a straight line and its speed changes with 5 m/sec. each one second.**

### Types of uniform acceleration

**Positive acceleration.****Negative acceleration.**

### Positive acceleration

**The object moves at a uniform positive acceleration (accelerating motion), when ****[Its initial speed < Its final speed]. ****Positive acceleration ****is an acceleration by which an object moves in a straight line when its speed increases by equal values ****through equal periods of time.**

**When a****n object moves at a positive acceleration equals 2 m/sec². ****This means that the object moves in a straight line and its speed increases by 2 m/sec, each one second. ****The sign (+) refers that the speed of the ****object increases regularly by 2 m/sec. each one second.
**

### Negative acceleration

**The object moves at a uniform negative acceleration (decelerating motion). [Its initial speed > Its final speed]. ****Negative acceleration ****is an acceleration by which an object moves in a straight line when its speed decreases by equal values through equal periods of time**

**When a****n object moves at a negative ****acceleration equals -2 m/sec². ****This means that the object moves in a straight line and its speed decreases by 2 m/sec each one second. ****The sign (−) refers that the speed of the object decreases regularly by 2 m/sec. each one second.**

**So, we can deduce the type of acceleration from the shape of the graph:**

**Positive acceleration:****when t****he object moves at (a non-uniform speed), V (initial) < V (final), So, it moves at an accelerating motion.**

**Negative acceleration:****The object moves at (a non-uniform speed), V (initial) > V (final), So, it moves at a decelerating motion.**

**Zero acceleration: The object moves at (a uniform speed), V (initial) = V (final).**

** The acceleration is positive when its value increases, while it is negative when ****its value decreases b****ecause when moving with a positive acceleration, the final speed is greater than the initial speed, while when moving with negative acceleration, the final speed is less than the initial speed.**

**The object which moves at a uniform speed, its acceleration equals zero. ****A body moves at zero acceleration because its speed doesn’t change by passing time (ΔV = Zero).**

### Problems

**• An object moves from rest and its speed reaches 20 m/sec. in 5 seconds. Calculate the acceleration of the moving object? What is the type of acceleration?**

**Solution**

**V₁ = 0 , V₂ = 20 m/sec. , Δt = 5 sec.
**

**a = V₂ – V₁ /Δt**

**a = (20- 0)/5= 4 m/sec² , ****Positive acceleration.**

**• A train moves at a uniform speed of 20 m/sec. When the driver uses the brakes, the train stops after 4 sec. Calculate the acceleration at which the train moves and mention the type of acceleration.**

**Solution**

**V₁ = 20 m/sec. ****V₂ = 0 , ****Δt = 4 sec**

**a = V₂ – V₁ /Δt**

**a= (0 – 20)/4 = – 5 m/sec² , ****It’s decelerating motion**

**• A car driver moves at a speed of 80 m/sec. used the brakes to make the car moves ****at a uniform decreasing acceleration 2 m/sec? Find the car speed after 12 seconds from using the brakes.**

**Solution**

**V₁ = 80 m/sec , ****V₂=56 m/sec , ****a = – 2 m/sec , Δt = 12 sec
**

**V _{2} = V_{1} + (a × t)**

**V₂ = 80 + ( – 2 × 12) = 56 m/sec
**

#### Guidelines to solve problems

**On moving at a uniform speed through the period of time (AB) and then followed by the movement at a uniform acceleration through another period of time (BC). So, The uniform speed through the period of time (AB) = The initial speed through the period of time (BC). ****[V₁ at point (B)].**

**• An object moves in a straight line at a regular speed. If the time taken by ****the object to move from (A) to (B) is 4 seconds, ****then it moves at a uniform acceleration from ****point (B) until it stops at point (C) in 20 seconds. Calculate each of the following: **

**The regular speed of the object to cover the distance (AB).****The uniform acceleration by which the object moves from point (B) to point (C).**

**Solution**

**1. Regular speed at (AB) = Distance/Time = 40/4= 10 m/sec.
**

**2. The initial speed at (BC) = The uniform speed at (AB) = 10 m/sec**

**The uniform acceleration at (BC) (a) = (V₂ – V₁)/At = (0 – 10) /20 = – 0.5 m/sec²**

**• A car moves at a speed of 60 m/sec., if the driver used the brakes to decrease the speed by 3 m/sec. Calculate the time after which the car stops?**

**Solution**

**V₁ = 60 m/sec, ****V₂ = 0 , ****a = – 3 m/sec² , ****Δt = ?**

**a = (****V₂ – V₁)/ Δt**

**Δt = V₂ – V₁/ a
**

**a = (0 – 60)/- 3
**

**a = 20 sec**

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**Physical Quantities, Scalars, Vectors, Distance, Displacement, Speed & Velocity**

**Motion in one direction, Types of Speed, Average Speed & Relative Speed**

**Types of motion, Relative motion, Applications of Mechanical waves & Electromagnetic waves**

**Role of waves in transferring energy, Wave Motion, Transverse waves & Longitudinal waves **

**Laws of circular motion (Centripetal Acceleration, Tangential linear Velocity & Centripetal Force)**