       In the previous chapter, we have analyzed objects with constant velocity. When the velocity of an object changes, the object is said to be accelerated. In this chapter, we will further analyze the motion and think about how fast an object moves, how far it moves and for how long.
 Support easyphysics.net by visiting our advertisers' websites. Section 1. What is acceleration? When an object's velocity changes, it accelerates. Acceleration shows the change in velocity in a unit time. Velocity is measured in meters per second, m/s, so acceleration is measured in (m/s)/s, or m/s2, which can be both positive and negative. Section 2. Average Acceleration and Instantaneous Acceleration

The average acceleration is the ratio between the change in velocity and the time interval.  For example, if a car moves from the rest to 5 m/s in 5 seconds, its average acceleration is An instantaneous acceleration is the change in velocity at one moment. We will study instantaneous acceleration more in depth later in the chapter.

 QUESTION: If a car accelerates from 5 m/s to 15 m/s in 2 seconds, what is the car's average acceleration? m/s/s QUESTION: How long does it take to accelerate an object from rest to 10 m/s if the acceleration was 2 m/s2? s QUESTION: Carl started to run at 10 km/h when he left his house. He arrived at school 30 minutes later. How fast was he running when he arrived there? Assume that his average acceleration was 30 km/h2. km/h Section 3. More Velocity-time Graph

Let's examine more about a velocity-time graph. We can say that the tangent of a velocity-time graph represents instantaneous acceleration since  For example, the instantaneous acceleration when t = 3 at the below graph is 3 m/s2, since the graph has a slope of 3 when t = 3. QUESTION: What is the instantaneous acceleration of the above object when t = 0? m/s QUESTION: What is the average acceleration of the whole trip? (When t = 7, velocity = 26 m/s) m/s/s QUESTION: Does above object has a constant acceleration? (Yes/No) Section 4. Displacement and Constant Acceleration

In this section, we will assume that acceleration is always constant.

We know that the area under the line of a velocity-time graph represents the displacement. Therefore, the equation  is true, where Vi is the initial velocity and Vf is the final velocity, since the area of a triangle is 1/2 * width * height. QUESTION: If a car accelerated from 5 m/s to 25 m/s in 10 seconds, how far will it travel? m The final velocity of a uniformly accelerated object is ,

where:

• Vf is the final velocity in m/s,
• Vi is the initial velocity in m/s,
• a is acceleration in m/s2, and
• t is time in second.

Therefore, by substituting it to the previous equation,  therefore, is true. If you don't understand the derivation, don't worry. The red formulae are the ones that you should learn.

 QUESTION: What is the displacement of a car whose initial velocity is 5 m/s and then accelerated 2 m/s2 for 10 seconds? m

From equations and , we can also say that  Therefore, is true. These four red equations are very important and you should be very familiar with them. (It doesn't mean that you should memorize these formulae. Learn by using them.)

 QUESTION: What is the final velocity of a car that accelerated 10 m/s2 from rest and traveled 180m? m/s ### Section 5. Acceleration Due to Gravity

Galileo was the first to find out that all objects falling to Earth have a constant acceleration of 9.80 m/s2 regardless of their mass. Acceleration due to gravity is given a symbol g, which equals to 9.80 m/s2.

Therefore, if you drop a pen, it should behave like this...

 Time (s) Velocity (m/s) Displacement (m) 0 0 0 1 9.8 4.9 2 19.6 19.6 3 29.4 44.1 4 39.2 78.4

For all previous equations, we can substitute g for a:    QUESTION: How long will it take for an apple falling from a 29.4m-tall tree to hit the ground? s ### Section 6. Chapter 3 Quiz

Take the Chapter 3 Quiz and see how well you can do!

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