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PHYS2001_Ch. 2

# PHYS2001_Ch. 2 - Ch 2 Kinematics in 1-D Mechanics...

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Ch. 2 – Kinematics in 1-D Mechanics Kinematics Dynamics Concepts needed to describe motion w/o forces Deals with the effects that forces have on motion Chs. 2 and 3 Ch. 4 Our goal is to describe the motion of some object. To do this, we must be able to specify its location in space at all times! In other words, what is the position of some object at time t ? Define Displacement : A vector which points from an object’s initial position to its final position.

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In this chapter, we will only consider 1 dimensional motion. Let’s look at the following example : At time t = t o , a jogger’s position relative to some fixed origin is x o . At some later time, t = t f , her position relative to the origin is x f . What is her displacement during this time interval? x origin x o t = t o t = t f x Her displacement, x , is the difference in her initial and final positions. x x is pronounced “delta x”, or “change in x”. Displacement = x = x f x o Units? The SI unit of displacement is the meter (m). In 1-D we can also talk about scalar displacement , which is just a number. It can be either positive or negative. For example, in the above problem, if x o = 10 m and x = 30 m, then her scalar
2.2 Speed and Velocity One of the most fundamental description of an object’s motion is its speed how fast its moving. If I run 30 m in 10 s, then my average speed is = 30 m 10 s = Distance Time = 3 m/s Units? The SI unit for speed is m/s . *Important concept → We are talking about constant speed , which means we will cover the same distance in the same time interval. Time Elapsed Distance Speed ave. = Speed tells us how fast an object is moving, but it doesn’t say anything about its direction of motion. Speed is a Scalar !!! Now let’s talk about average velocity .

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Velocity is a vector ! It tells you both the speed and the direction the object is moving! Time Elapsed Distance Speed ave. = Time Elapsed nt Displaceme Velocity ave. = Average velocity is represented by v , where t x t t x x v o f o f = - - = Like speed, the units of velocity are m/s. Speed and velocity are often used interchangeably, but speed is a scalar and velocity is a vector. Speed is the magnitude of velocity, i.e. it’s the length of the velocity vector. v x = Speed
Example : A squirrel runs at constant speed from the base of an oak tree and without stopping retrieves an acorn and returns to the tree. The acorn is 25 m away, and it takes the squirrel 4.7 s to do this. What are the average speed and velocity of the squirrel? 25 m Define the x-axis as the direction in which the squirrel moves. x = 0 x = 25 x Time Distance Speed = m/s 6 . 10 s 4.7 m) (2)(25 = = Time nt Displaceme Velocity = t x t t x x o f o f = - - = ! m/s 0 s 7 . 4 0 0 = - = His average velocity is zero , since his initial and final positions are the same!

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Which of the following statements could be correct? (a) The car traveled around the track at constant velocity. (b) The car traveled around the track at constant speed.
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PHYS2001_Ch. 2 - Ch 2 Kinematics in 1-D Mechanics...

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