Translational motion

Question 1

What are vectors and scalars?

Answer 1

Scalars: Magnitude only

Vector: Magnitude and direction

Question 2

Describe the addition of vectors in plain words

Answer 2

• Draw the two vectors on a common scale on an angle to each other
• Connect the tail of the first to the head of the second, this vector is the sum, or resultant vector

(trigonometry is used in determining the magnitude/direction of the resultant vector)

Question 3

Describe the subtraction of vectors in plain words

Answer 3

• Reverse the direction of a vector

- Then add it to the other as you normally would (head to tail vector is resultant vector difference)

Question 4

How can a vector be resolved into its scalar components?

Answer 4

• Plot vector on coordinate axis
• Resolve into x-component and y-component:

Where a = vector magnitude and θ = vector angle

ax: a(cosθ)
ay: a(sinθ)

Question 5

Describe the unit vector and give the equation for a 2D vector (ie vector a) split into its component parts

Answer 5

A unit vector gives a symbol for a vector component as follows:

i: x-direction
j: y-direction
k: z-direction

a = iax + iay

(scalar components = ax, ay)

Question 6

What does SohCahToa mean? How is it used?

Answer 6

It helps memorize the use of cos, sin and tan functions. Can be used to determine angles

sinθ: opposite/hypotenuse: y/r

cosθ: adjacent/hypotenuse: x/r

tanθ: opposite/adjacent: sinθ/cosθ: y/x

Question 7

List the three functions for cotangent, secant and cosecant

Answer 7

cotangent: cotθ: x/y
secant: secθ: r/x
cosecant: cscθ: r/y

Question 8

If cos(x°) equals 1/2, than how do you determine x?

Answer 8

Using the inverse function (cos^-1)

(cos^-1)(1/2) = 60°

Question 9

Of distance and displacement, which is scalar and which is vector?

Answer 9

Scalar: distance
Displacement: vector

Remember: Scalars are always positive

Question 10

What is the instantaneous velocity of a system?

Answer 10

The slope of the graph of the displacement of that system vs. time at that time

Question 11

Give the simplest formula for acceleration

Is acceleration a vector or scalar?

Answer 11

a = v/t

acceleration = (velocity)/(time)

It is a vector, and it has a direction (ie. acceleration and deceleration) and a magnitude (ie. m/s^2)

Question 12

How can the instantaneous acceleration be determined?

Answer 12

By calculating the slope at a specific point on a velocity vs. time graph. Or by taking the limit when Δt approaches zero. On a average acceleration formula.

Limits are not doable on MCAT. Must find instantaneous acceleration by:

a = Δv/Δt