Motion in One Dimension Unit 1.1 Motion in One Dimension

One Dimensional Motion One dimensional motion is the simplest form of motion. It is motion that takes place in one direction.

Example: train moving on a track Movement is either forward or backwards.

Motion takes place over time and depends upon the frame of reference.

Frame of Reference The Earth is spinning on its axis, so that train, stations and the tracks are moving around the axis. At the same time, the Earth is moving around the Sun. The Sun and the rest of the solar system are moving through our galaxy. The galaxy is traveling through space as well.

Frame of Reference Whenever faced with a complex situation like this, physicists break it down into simpler parts. One key approach is to choose a frame of reference against which you can measure changes in position.

Frame of Reference In the case of the train, the stations along its route are convenient frames of reference. If an object is at rest, the position does not change with respect to a frame of reference.

Frame of Reference In physics, any frame of reference can be chosen as long as it is used consistently. If you are consistent, you will get the same results no matter which frame of reference you use.

Displacement is not always equal to the distance traveled. As any object moves from one position to another, the length of a straight line from its initial position to the object’s final position is called the displacement. ∆x = xf - xi Displacement is not always equal to the distance traveled.

Displacement I drive 20 miles south on highway 16. I turn around and drive 10 miles north on highway 16 then drive 40 miles south again. What is my displacement?

Displacement 50 miles

Displacement Displacement can be positive or negative based on the direction. For our purposes assume that the right or upward motion will be positive and that left or downward motion will be negative.

Velocity Displacement does not completely describe the motion of an object. Knowing the speed is important when evaluating motion.

Velocity The average velocity is defined as the displacement divided by the time interval of displacement. In SI, the unit of velocity is meters per second, abbreviated as m/s. vave = ∆x = xf - xi ∆t tf - ti

Velocity The average velocity of an object can be positive or negative, depending on the sign of the displacement. Time interval is always positive.

Example The value is an average. Consider a car trip to a friend’s house 370 km to the west along a straight highway. If you left your house at 10 am and arrived at your friend’s house at 3 pm, your average velocity would be as follows:   -370 km = -74 km/h 5.0 h The value is an average.

Velocity The average velocity is equal to the constant velocity needed to cover the given displacement in a given time interval.

Velocity Velocity is the not same as speed. In everyday language, the terms speed and velocity are used interchangeably. In physics, there is a difference. Velocity describes direction and magnitude whereas speed is only magnitude. Average speed = distance time

Velocity Velocity can be interpreted graphically. The velocity of an object can be determined if its position is known at specific times along its path.

Velocity One way to determine this is to make a graph of the motion. Slope = rise = change in vertical coordinates run change in horizontal coordinates

Velocity Different types of velocity green represents negative velocity pink represents positive velocity red represents zero velocity  

Instantaneous Velocity Instantaneous velocity may not be the same as average velocity. Instantaneous velocity is the velocity of an object at some instant or a specific point in its path.

Instantaneous Velocity Now consider an object whose position versus time graph is not a straight line but a curve. The object moves through larger and larger displacements as each second pass. Thus, its velocity increases with time.

Instantaneous Velocity One way to determine the instantaneous velocity is to construct a straight line that is tangent to the position versus time graph at that instant.

Instantaneous Velocity

Instantaneous Velocity The slope of this tangent line is equal to the value of the instantaneous velocity at that point. You can verify some of these values by carefully measuring the slope of the curve.