Re: GAMSAT Physics Translational Motion
Scalars and Vectors
Knowing the difference between vectors and scalars will be advantageous when solving physics problems in the GAMSAT. A vector is a physical quantity that has both direction and magnitude; a scalar is a physical quantity that has magnitude but no direction.
Arrows can be used to reveal the direction of the vector. The length of the arrow will reveal the magnitude of the vector.
Adding and Subtracting Vectors
When adding vectors, the head of the first vector is placed to the tail of the second vector. An arrow is drawn from the tail of the first to the head of the second. The resulting arrow represents the vector sum of the other two vectors.
For the subtraction of vectors, place the heads of the two vectors together and draw an arrow from the tail of the first to the tail of the second. The resulting arrow represents the vector difference between the two vectors.
Resolution of Vectors and Trigonometric Functions
A vector can be divided into two components. These two components are perpendicular to each other. A vector is resolved into its scalar components. The lengths of the component vectors are found through Pythagoras Theorem and Trigonometric Ratios.
This skill is required in projectile motion problems in the GAMSAT. It is essential that students are able to understand and apply Pythagoras Theorem and Trigonometric Ratios.
Distance and Displacement
Distance and displacement are respectively scalar and vector components. Displacement is distance with an added dimension. This added dimension is direction.
Simply put, we can say that distance refers to how much ground an object has covered and displacement is the object’s overall change in position.
To test your understanding of this distinction, consider the motion depicted in the diagram below. A lady walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.
Even though the lady has walked a total distance of 12 meters, her displacement is 0 meters. During the course of her motion, she has “covered 12 meters of ground” (distance = 12 m). Yet when she is finished walking, she is not ‘out of place. In other words, there is no displacement for her motion (displacement = 0 m). Displacement, being a vector quantity, must give attention to direction. The 4 meters east cancels the 4 meters west; and the 2 meters south cancels the 2 meters north. Vector quantities such as displacement are direction aware. Scalar quantities such as distance are ignorant of direction. In determining the overall distance traveled by the lady, the various directions of motion can be ignored.
Speed and velocity
Speed and velocity are respectively scalar and vector components. Velocity is speed with the added dimension of direction. The units for velocity are expressed in length divided by time – e.g. meters/sec (m/s); feet/sec; miles/hour.
The following two equations must be memorised for the GAMSAT.
Speed = distance/time
Velocity = displacement/time
Acceleration is the rate of change in velocity. Acceleration is a vector, meaning that it has a direction and a magnitude. An object is accelerating if it is changing its velocity. The units for acceleration are expressed as velocity divided by time such as meters/sec2.
When an object experiences negative acceleration it is termed deceleration.
The formula for acceleration must be memorised for the GAMSAT.
Acceleration = rate of change of velocity/time.
Uniformly Accelerated Motion
Uniformly accelerated motion is motion that involves constant acceleration. Constant acceleration means that both the magnitude and direction of acceleration must remain constant. A particle that exhibits uniform accelerated motion will always accelerate at a constant rate. When this particle is accelerating on a linear path, there are 4 variables that can describe its motion. These are:
Time (t) – scalar
Displacement (x) – vector
Velocity (v) – vector
Acceleration (a) – vector
Three basic equations can be used to derive the values of these variables. These equations are usually provided on the GAMSAT stimulus material, but they should be memorised for speed and efficiency. Manipulation of these equations will become second nature through repetition and practice.
The linear motion equations are as follows:
x = xo + vot + 1/2at2
v = vo + at
v2 = vo2 + 2ax
When deciding which equation to use, choose the one for which you know the value of all but one of the variables.
Remember: constant acceleration and linear motion are required in order to use these equations.
Another important concept in the GAMSAT is average velocity. When an object experiences uniformly accelerated motion the average velocity can be determined using the following formula:
Vavg = ½(v + vo)