Velocity and Speed

Acknowledge the difference between Scalar and Vector Quantities

A scalar quantity is a quantity that only gives the magnitude and not the direction, whereas a vector quantity is a quantity that gives the magnitude as well as the direction.

Understanding the difference between Displacement and Distance
Distance:

Distance is a scalar quantity that refers to how much ground has been covered during an object’s motion

Displacement:

Displacement is a vector quantity refers to how far the object has moved compared to where it was at the beginning

Example:
Let’s take this image as an example. A person walks 4m east, 2m south, 4m west, and 2m north. He has walked a total of 12m (4m + 2m + 4m + 2m), however, his displacement is 0m, as he has not moved anywhere from his starting point

Apply the relationship: average speed = distance/time
The formula to find the average speed of an object going in a straight line can be found by taking the distance it went, divided by how long it took to go that distance (distance/time). The same can be applied inversely. To find the time, you would do distance/speed, and to find the distance, you would do time x speed.

Question 1: A car drives 120km in 3hrs, calculate the average speed in km/h
First of all we can see in the equation that we’ve been given the distance and the time. That means we have to figure out speed. When we refer to the triangle, we see that speed is equal to distance divided by time. So all we have to do is plug in our values as so: s = 120/30 and simplify to get our answer of 40km/h.

Question 2: A lorry travels 100km at an average speed of 25km/h, Work out how long the journey lasted.

In this question we are presented with distance and speed, meaning we need to find the time. In the triangle it shows that time = distance divided by time. Hence we plug our values into the equation to become t = 100/25 which gives us 4hrs. The unit is hours since the speed is kilometers per hour.

Scalar and Vector Quantity of Distance (m)

Distance is a scalar quantity meaning that it only gives a magnitude and does not specify direction. Distance is measured in meters.

The vector quantity of distance is displacement, in which both the magnitude and direction is specified. This is also measured in meters but when asked the displacement of an object, the magnitude and direction must be stated.

Scalar and Vector Quantity of Speed (m/s)

Speed is also a scalar quantity meaning that it only gives the magnitude and not the direction. Speed is measured in meters per second because speed is equal to distance over time.

The vector quantity of speed is velocity in which both the speed is mentioned as well as the direction of the speed. Velocity is also measured in meters per second but once again must specify both speed and direction.

Define the terms ‘speed’, ‘velocity’, and acceleration
Define Speed

Speed (s) is defined as the distance traveled in a timeframe. The formula is s = d/t and the S.I. unit is m/s. Speed is a scalar quantity since it only takes the magnitude into account

Define Velocity

Velocity (v) is defined as the displacement covered in a timeframe. The formula is v = Δs/Δt and the S.I. unit is m/s. Velocity is a vector quantity since it takes displacement into account, which is a vector quantity.

Define Acceleration:

Acceleration (a) is defined as the change in velocity over time. The formula is a = Δv/Δt and the S.I. unit is m/s2. This must mean that acceleration is a vector quantity as it takes into account velocity and velocity is a vector quantity.

Contrast and explain the difference between speed and velocity

The main difference is that speed does not take direction into account (making it scalar) while velocity does take direction into account (making it vector).

Recall that acceleration is measured in meters per second squared (m/s^2)

The reason why acceleration is m/s^2 is because acceleration is velocity over time. The velocity is measured in m/s and time is measured as s which means acceleration is m/s / s = m/s^2.

Solve Acceleration Equations:

To refresh, the equation for acceleration is a = Δv/Δt.

Question: A car accelerates from 0km/h to 36km/h in 20secs. What is the acceleration of the car in m/s^2?

First identify the variables and plug it into the equation to get a = (36-0)/20 which simplifies to a = 36/20. Because the unit asks for m/s^2, we have to convert 36km/h to m/s. This is done by multiplying 36 by 1000 (to convert 36km to m) and dividing it by 3600 (to convert h to s) which turns our equation to (36 x 1000)/3600 which simplifies to 10m/s. Now to revert back to the original equation, we can add our new value and divide it by 20 to become 10/20 which gets us 0.5m/s^2

Graphs:

There are three main types of graphs: Displacement-time graphs, Velocity-time graphs and Distance-Time graphs. One pattern you will see is that only the y-axis unit is changing whilst the x-axis is constant to time.

How to Calculate Gradient in Graphs
Displacement-Time graphs in terms of velocity

Gradient = change in displacement / change in time (Δs/Δt = Velocity)

Velocity-Time graphs in terms of acceleration
Gradient = change in velocity / change in time (Δv / Δt = Acceleration)

Distance-Time graphs in terms of speed
Gradient = Change in Distance / Change in Time (Δd/Δt = Speed)

Analyse displacement–time graphs in terms of velocity
The gradient in a displacement-time graph represents the velocity of an object at that time. On the contrary, in a velocity time graph, the gradient represents acceleration of an object. The area under the curve of a speed-time graph is distance covered. The area between the normal (line of x=0) and the curve in a velocity-time graph is displacement.

Annotate and Analyze a Velocity-Time Graph

The orange line represents positive acceleration since it’s a line moving in both velocity and time. It is positive because the difference in velocity is positive.
The green line represents zero acceleration since there is no velocity. This means the object is at rest

The blue line represents negative acceleration since it’s a line moving in both velocity and time. It is negative because the difference in velocity is negative.

In order to calculate the displacement we have to calculate the area under the line(s)

1. Area of Positive Acceleration (triangle)
(b x h)/2     b = time taken | h = change in velocity
= (10 x 5)/2 = 50/2 = 25m

2. Area of Zero Acceleration (rectangle)
L x W = 5 x 10 = 50m

3. Area of Negative Acceleration (triangle)
(b x h)/2     b = time taken | h = change in velocity
= (10 x -5)/2 = -50/2 = -25m

SUVAT Equations:

The SUVAT Equations are a set of 5 equations that are used for dealing with motion. SUVAT is an acronym that stands for the 5 variables used in the equations:

• S = Speed
• U = Initial Velocity
• V = Final Velocity
• A = Acceleration
• T = Time

If any four of the variables are known, then the 5th variable can be solved through using these equations

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