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# Velocity and acceleration

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provides an overview of the topic of motion in physics

teaches students about the idea of velocity and acceleration

Explains the idea of gradient and goes in-depth into interpretation of distance-time and velocity-time graphs

Provides exercises to test the understanding of students

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### Velocity and acceleration

1. 1. VELOCITY AND ACCELERATIONActually everything in the world is either at rest or movingFor a moving object, you can characterise its movement by1) how fast it is going2) thedirection it is heading towardsThe word velocity actually includes tells you both how fast an object is going, as well as itsdirection.This is important, because in the absence of friction or other type of forces, Newton theorisedthat an object will travel in a straight line (in other words, same direction) and at a constantspeed.What this means is that so long as either1) an object slows down or speeds up2) an object’s direction of motion changesThen there is a change of velocity.Newton theorised that a change of velocity can only be caused by applying a force on anobject.He also felt that objects with more mass have more inertia. The more the inertia, the moredifficult it is to change its motion.An oil tanker is a great example of inertia at work!Since an oil tanker doesn’t not have brakes,it has to set its propeller to propel the ship backwards. There is a change in velocity there, andthe tanker’s large mass allow it to resist the change in motion such that it takes a tanker 10kmbefore it can grind to a halt.The formula F = ma relates this idea. a refers to acceleration which refers to any change invelocity. a is affected by mass… the larger the mass, the smaller the change in velocity!Graphs can help us understand information easily and is often used to represent velocity anddistances over a time period. In a sense, a graph is like a storybook, telling you a story ofwhat happens from the start till the end. From this graph, it tells a quite boring story that the person or object repeated what he was doing for 240 seconds As the distance covered by the guy increased by 1000m every 40s for 240s, he was clearly travelling at a constant speed throughout. You could represent his speed on a speed time graph that looks like this
2. 2. This story you can see is also the same one, the speed did not change at all for the whole 240seconds. Yet the slope of the graph is very useful when we are comparing one thing against another. We can precisely measure the relationship between the y-axis thing and x-axis thing by taking the rise divide by the run. This tells us that for every unit on the x-axis, how many units would be reflected on the y-axis Such as in 10m/s, every second the distance increase by 10m If A and B represent 2 different cars, which car is travelling faster? _________How can we tell which is the faster car?____________________________________________________________________________________________________ Over here in the next graph, what is story that you can see? The object is at rest and its velocity is 0m/s For graph (iii), notice that if you try to measure the gradient, you will find that thegradient is different and it gets larger as time progresses.This indicates that the distance per unit time is increasing…and shows that the velocity is increasing. For graph (iv), the gradient (rise over run) is constant, this means that distance per unit time is the same… And so, the velocity is constant. To better understand what increasingvelocity got to do with distance travelled, look at how faraway the object on the left is from the starting position astime goes by.
3. 3. Take after 5s for example, the object travelled 50m or 10m every second, yet it only travelled2m on the first second, and most of the 50m was travelled in the last 2 minutes… This is a velocity-time graph. Notice that velocity is _____________. Can you calculate the relationship between velocity and time? _________________ What will happen in the following scenario? The change in velocity is in the same direction as velocity. Therefore, velocity will increase. The change in velocity is in the opposite direction as velocity.Therefore, velocity will decrease1a) A bus travels at a constant velocity forward of 12m/s for 5hours, how would you plot velocity versus time in a graph?1b) Acceleration of 4m/s2 means that the speed of an object will change by 4m/s every s!1c) What is the final speed of the bus above if it accelerates forward at 4m/s2 for 20 seconds?1d) What is the final speed of the bus above if the driver steps on the brake and the bus slowdown by at 4m/s2 for 2 seconds?2) If a car start moving from rest and accelerated at 3.5m/s2 for 10 seconds, what is itsvelocity after 10 seconds?
4. 4. 3) A Cheetah was jogging at 7m/s when it saw a nice prey walking around the area andstarted giving chase. The Cheetah reached a top speed of 70m/s in 9 seconds. What is itsacceleration?Speed-time graph Between time 0s to 4s, the person is travelling at ________________________ Between time 4s to 9s, the person is travelling at __________________________Notice that the formula for speedSo distance travelled = speed x time takenTherefore, the distance travelled by the person in the diagram above is also the area under thegraph.4) Find the distance travelled by the person between 0s to 9s5) Sketch the distance time graph for the distance travelled for the moving object representedby the graph
5. 5. Between time 0s to 4s, the velocity of the runner is ______________This means that ____________________ must be occurring at _______m/s2Between time 4s to 8s, the velocity of the runner is _______________This means that there is no __________________________ because there is____________________________________________From 8s to 10s, the velocity of the runner _____________. This means that_____________________ must be occurring at m/s2Sketch the distance time graph for the runner.F = MA