Lesson 1 Vectors

What is the displacement curve?

(x*final*) - (x*initial*) = (v*initial*)x(time) + (1/2)(acceleration)(time^2)

What is a reference frame and how does it relate to a person outside staring at a train moving 30 km/h vs. two people standing inside that same train?

A reference frame is used to represent what you should base your measurement off os (from what perspective) A person outside the moving train will see the people moving at 30 km/h along with the train. Two people inside the moving train will see each other as being stationary and not moving at 30 km/h.

How is acceleration calculated from velocity?

Acceleration = change in velocity/time

How is average velocity calculated from displacement?

Average velocity = displacement/change in time

If we know the angle of a vector and adjacent horizontal vector, how can we use that to find the length of the original vector?

By using cos(angle) = adjacent/hypotenuse

Johnny drove 17 miles in 20 minutes. His total displacement, however, was only 10 miles in the north direction. What was his average velocity?

Displacement = 10 miles Time = 20 minutes (1/3 hour) Average velocity = displacement/change in time Average Velocity = (10 miles) / (1/3 hour) Average Velocity = 30 mph

Scalar is to distance as vector is to___________? What happens if one person travels 10 m from the starting point and back to the starting point?

Displacement. Displacement includes a direction and therefore it is a vector quantity. Distance, on the other hand, is a scalar quantity. Person: distance = 10m, displacement = 0m

What are the three ways to find instantaneous velocity without using calculus?

If the speed is constant, then it is that speed. The slope of a displacement vs. time graph at that point If the acceleration is constant, use a kinematic equation: v=(v*initial*)+(acceleration)(time) v^2= (v*initial*)^2 + 2(acceleration)(change in x)

What does instantaneous mean when referring to velocity (or speed of acceleration, etc)?

It means the velocity at a specific time, not an average over a period of time.

Lesson 1: Vectors

Lesson 1: Vectors

How can you solve for the horizontal and vertical components of a vector?

Make a right triangle and use soh can toa (you will also need to know the angle)

What does soh cah toa stand for?

Sin = opposite/hypotenuse Cos = adjacent/hypotenuse Tan = opposite/adjacent

What does the slope at a point on a position vs time graph represent?

The instantaneous velocity at that point.

How do you add vectors together?

The tail of one vector gets added to the head of another vector and the distance between the two points is measured.

Johnny is running at 1 m/s in the positive direction. Over 20 seconds he increases his speed to 2 m/s, what is his average acceleration?

Time = 20 seconds Change in velocity = (2 m/s - 1 m/s) = 1 m/s Acceleration = change in velocity/time Acceleration = (1 m/s)/ (20 s) Acceleration = 0.05 m/s^2

What is the cross product of two vectors used for?

To create another vector

What is the dot product of vectors used for?

To generate a scalar

How can you break down a two dimensional vector into one dimensional vectors?

Two dimensional vectors can be broken down into their horizontal and vertical components

What does vector b̂ = 4î + 3ĵ mean?

Vector b can be broken down into a horizontal vector of length 4 and a vertical vector of length 3

What is the difference between a vector and a scalar? Provide examples of each.

Vector is has magnitude AND direction. Examples include displacement, force, and acceleration. Scalars just have magnitude. Examples include temperature, speed, distance.

What is the difference between velocity and speed?

Velocity is a vector quantity, while speed is a scalar quantity. Speed = absolute value of velocity.

If you drop ball A and ball B at the same time, but ball A has a horizontal vector component, while ball B is just thrown straight to the ground, will they land at the same time?

Yes because the horizontal component is separate from the vertical component.

If Johnny got in his car and traveled northwest, with a 60 degree angle between his direction and due west, how far west would he have gone if he went 5 miles in the northwest direction?

angle = 60 degrees hypotenuse = 5 miles cos(angle) = adjacent/hypotenuse cos60 = adjacent/5 5*cos60 = adjacent 2.5 miles west = adjacent