Kinematics is the study of moving objects. This includes objects moving at a constant speed and

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Mechanics Kinematics Kinematics is the study of moving objects. This includes objects moving at a constant speed and those that are changing velocity i.e. accelerating.

Important factors to understand when solving kinematic problems are:

Vector – a vector is a value with a direction. For example, if you’re driving 50km/hr North, this is a vector value as it has a direction (north). If I say 50km/hr without specifying the direction, this is called the scalar value.Speed – how fast something is going. Speed is always a ‘scalar quantity’ meaning it never has a direction.Velocity – the vector quantity of how fast something is going e.g. 50km/hr, North. When an object is either travelling in one direction or the opposite direction, the velocity is often depicted with a plus or minus value.Acceleration – how fast the velocity of an object is changing. Acceleration is a vector quantity. In general, when the acceleration is negative this means an object is slowing down (or, decelerating). When the acceleration is positive it means it is speeding up.Distance – how far something has moved. A scalar quantity.Displacement – how far something has moved in a certain direction. This is a vector quantity.Time – time is always a scalar quantity.Kinematics is about finding one of the above values of an object with the information you know.For example, if you know the speed of a vehicle and how long it’s been driving, you can figure out the displacement it’s travelled.This is where kinematic equations come in. There are essentially on 2 equations (and 2 variations of them) you should know for our purposes. 3 / 4

• Where ‘v’ is velocity, ‘d’ is displacement and ‘t’ is time. Velocity is equal to the

displacement over time.

• . Acceleration is equal to the change in the velocity over time.

Let’s focus on equation 2. for now, with an example.Example: A car starts from stationary and gets to 36m/s in 4 seconds. The t = 4s, and the v Δ = the final velocity – the initial velocity = 36 – 0 = 36.a = 36 / 4 = 9 m/s 2 This equation can also be written as seeing as v Δ (‘a change in velocity’) is the final velocity minus the initial velocity.Note that when solving these problems, it is extremely important to have the vectors in the right direction. It is thus advisable to draw diagrams indicating the direction of movement in kinematic problems.Let us now look at equation 1, . This equation is simple to understand when an object is moving at a constant speed. What if the car is constantly slowing down and speeding up? In such cases, this equation still holds, but it must be slightly modified to vaverage = d/t. That is, displacement over time is equal to the average velocity that the car is travelling.So how do you calculate the average velocity? The average of anything is the maximum value minus the minimum value divided by two.For a situation like in Example 1, the car is speeding up, so the maximum velocity, vmax, is the final speed, vf, and the minimum velocity, vmin is the initial speed, vi. Therefore. Vaverage = (vf- vi ) / 2.Therefore, for a situation where an object is accelerating uniformly, (Vf – vi)/2 = d/t .We can rearrange this to make displacement, d the subject.In situations where the initial velocity is zero, acceleration is equal to vf over t. So if we substitute a for vf in the above equation… Note that this only holds when the initial velocity is zero.This is all the kinematic equations you need to know. Any others kinematic equations are simply derivatives of the above.

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