Kinematics: Displacement and Velocity
Vectors and Scalars Most measurements that you use in everyday life are called scalar quantities, or scalars. These quantities have only a magnitude, or size. Mass, time, and energy are scalars. The distance an object travels and also the speed at which it travels are scalar quantities.
Vectors and Scalars In physics, however, you will usually describe motion in terms of vector quantities, or vectors. In addition to magnitude, vectors include direction. The position, displacement, velocity, and acceleration of an object are vector quantities
Scalar quantities Vector quantities Quantity Example Distance 15 km Displacement 15 km [45° N of E] Speed 30 m/s Velocity 30 m/s [S] Time interval 10 s Acceleration 9.81 m/s2 [down] Mass 6 kg Force 2400 N [30° above horizontal] Energy 3600 J
Displacement Displacement is the vector difference of the final position and the initial position of an object.
Velocity Velocity is the quotient of displacement and the time interval.
Kinematics: Graphical Analysis
Determining the slope of a linear graph Recall: Graph of Velocity versus Time velocity (m/s [East]) time (seconds)
Determining the area under the graph Recall: In this case, the shape of the shaded area between the line and the x-axis is a triangle. Graph of Velocity versus Time velocity (m/s [East]) time (seconds)
Determining the slope of a curved-line graph Determine the instantaneous velocity at 7.5 s. First, draw tangent line on graph at 7.5 s. Then, determine the slope of the tangent line. Graph of Position versus Time position (metres [North])
Determining average velocity on curved line position-time (d-t) graph Determine the average velocity between 7.0 and 14.0 h. First, draw straight line between 7.0 and 14.0 h. Then, determine the slope of the line.