Final answer:
To solve vector displacement problems, break each displacement into eastward and northward components using cosine and sine, respectively, then sum the components. Average speed is total distance divided by time and doesn't include direction, while average velocity is total displacement divided by time and includes direction.
Step-by-step explanation:
To solve the problems involving vector displacement, you need to use the graphical technique for adding vectors. This involves breaking down each vector into its x (eastward) and y (northward) components using trigonometric functions such as sine and cosine.
A person walks 25.0 m at an angle 49.0° north of east, followed by 23.0 m at 15.0° north of east, and then 32.0 m at 68.0° south of east. Each displacement vector is broken into components. For example, the first displacement has an x-component of 25.0 m × cos(49.0°) and a y-component of 25.0 m × sin(49.0°). All x-components and y-components are then summed separately to find the total displacement in the east-west and north-south directions, respectively. The overall displacement vector's magnitude and direction can then be determined using Pythagorean theorem and trigonometry.
In contrast, average speed is a scalar quantity calculated by dividing the total distance traveled by the time taken. The caveat is that, unlike average velocity, it does not have a direction. Average velocity, on the other hand, is a vector quantity and requires both a magnitude and direction. It is calculated by dividing the total displacement by the time taken, and its direction is the same as that of the total displacement vector.
Acceleration is also a vector quantity and indicates changes in velocity with time. If an object accelerates in a direction opposite to its velocity, like 8.33 m/s² due west for a horse, it means the object is slowing down in the eastward direction or speeding up westward.