Kinematics

Question 1

The big five

Answer 1

d = 1/2(v_o + v_f)t

v_f = v_o + at

d = v_ot + 1/2at²

d = v_ft - 1/2at²

v_f² = v_o² + 2ad

Question 2

Free Fall Projectile:

equation for distance/discplacement (x), velocity (v_x), and acceleration (a_x).

Answer 2

x = v_oxt

v_x = v_ox

v_ox = v_ocos(theta)

a_x = 0

Question 3

Free Fall Projectile Motion

Give the equation for distance traveled in y direction (y), velocity in y direction (v_y), and acceleration (a_y)

Answer 3

y = v_oyt + 1/2(-g)t²

v_y = v_oy + (-g)t

v_oy = v_osin(theta)

v_y = 0 at peak

a_y = -g

*Note that some are the same as the big five

Question 4

Equation for velocity, acceleration, and force

Answer 4

v = ∆x/t

a = ∆v/t

F = ma = m∆v/t

Question 5

If acceleration is constant, what equation can you use to find average velocity?

Answer 5

v_a = (v_f - v_i) / 2

Question 6

If velocity is constant, then acceleration is ___

Answer 6

0

Question 7

If velocity is constant, then net force is ____

Answer 7

0 (because acceleration is 0)

Question 8

What is Newton’s first law?

Answer 8

F = ma

object at rest will stay at rest and object in motion will stay in motion unless acted upon by another (unbalanced) force.

therefore, F_net = 0 when v is constant

Question 9

What is Newton’s second law?

Answer 9

∑F = sum of all the forces in all directions = F₁ + F₂ + F₃ +…

An object experiencing a net force will experience an acceleration in that direction.

Question 10

What is Newton’s third law?

Answer 10

F_{1 on 2} = F_{2 on 1}

F_A = - F_B

every action has an equal and opposite reaction

Question 11

Analyzing the equation F = ma

1) If F_net is constant and you decrease the mass by half, how will this affect acceleration?
2) If the mass stays constant, and the F_net doubles, how will this affect acceleration?

Answer 11

1) a will double in value

F = ma ⇒ m = F/a ⇒ 2m = F/a ⇒m = (1/2)F/a aka m = F/2a

2) a will double because F_net and a are directly proportional

Question 12

How do you find the net force in the x and y direction?

F_net,x = _______

F_net,y = _______

Answer 12

F_net,x = ma_x = macos(theta)

F_net,y = ma_y = masin(theta)

Question 13

Equation to find the force of gravity on an object?

Answer 13

F = mg

*Note this is equal to the weight of the object

Question 14

Equation for force of static and kinetic friction

Answer 14

F_f,s ≤ µ_sF_N

F_f,k = µ_kF_N

Question 15

On an inclined plane, how do you find the F_g and the F_N?

Answer 15

F_g = mg

F_N = mgcos(theta)

Question 16

Is it possible for a car to have the same velocities but different speeds?

Answer 16

No

Question 17

Distinguish between velocity and speed

Answer 17

velocity is the change in discplacement over time

speed is the total distance traveled over time

Question 18

Will someone’s velocity always be the same numerical value as their speed?

Answer 18

No

If a person runs around a track and stops where they started, their discplacement will be zero, which means their velocity will be zero; however, their average speed will actually have a numerical value

Question 19

acceleration is how fast an object’s ____ changes over time

Answer 19

velocity

Question 20

Can an object be accelerating even if it’s speed is constant?

Answer 20

Yes, because velocity is not speed. velocity is discplacement over time. So an object can have a consistent speed but be changing direction, which means acceleration is also changing.

Question 21

If the acceleration vector is parallel and in the same direction (or has the same sign) as the velocity vector, the object’s speed is _____

Answer 21

increasing

(direction remains constant)

Question 22

If the acceleration vector is in the opposite direction or has the opposite sign of the velocity vector, the object’s speed is ____

Answer 22

decreasing

(direction remains constant)

Question 23

If the acceleration vector is perpendicular to the velocity vector, this means that the object’s speed is ____ and that it’s direction is _____

Answer 23

speed is constant

direction is changing

Question 24

If the acceleration vector has an angle 0-90 or 90-180 compared to the velocity vector, what does this say about the object’s speed and direction?

Answer 24

speed is either increasing or decreasing (same direction or sign is increasing, opposite direction or sign is decreasing)

direction is changing

Question 25

If a dog runs 3m north and 4m west in 1sec, what is the speed of the dog?

What would be the discplacement of the dog?

What is the dog’s average velocity?

Answer 25

speed = 3m + 4m / 1sec = 7m/s

the dog’s path makes a right angle, which means the discplacement vector would be 5m northwest (3,4,5 triangle)

v = 5m/1sec = 5m/s

***Note speed and velocity do not have the same numerical value

Question 26

what is uniformly accelerated motion?

Answer 26

This is motion in which the object’s acceleration is constant

Question 27

How can you find discplacement using an object’s average velocity (assuming that acceleration is constant)?

Answer 27

multiply it by time

v = ∆d/∆t

⇒ d = v·t

Question 28

The slope of a position vs time graph gives you ____

Answer 28

velocity

Question 29

The slope of a velocity vs time graph gives the _____

Answer 29

acceleration

Question 30

The area under a velocity vs time graph gives you the objects ____

Answer 30

discplacement

Question 31

In projectile motion, the horizontal velocity will be _____ throughout the entire flight. Why?

Answer 31

constant

because there is no acceleration force in the horizontal direction. the only acceleration force will be d/t gravity, which is in the y direction

Question 32

In projectile motion, how do you find the distance an object travels?

Answer 32

x = v_oxt

aka distance = initial horizontal velocity x time

Question 33

For projectile motion, what is the vertical velocity when the object reaches the top of it’s parabolic path?

Answer 33

the vertical velocity will be zero; however, note that just because the vertical velocity is zero, the object still has horizontal velocity. Thus, the object’s average velocity is not zero at the top of the parabola

Question 34

For projectile motion: If the object takes 3 seconds to reach the top of it’s trajectory, how many seconds will it take to fall to the ground?

Answer 34

3 seconds

the top of the trajectory is half of the parabola, and each half of the parabola is a mirror image of one another. Hence, whatever time it takes to reach the top of it’s trajectory will be the same amount of time it takes to reach the ground. Hence, the total flight time will be double of what it takes to reach the top.

Question 35

In a crash simulation, a car traveling at x m/s can stop at a distance d m with a maximum deceleration. If the car is traveling at 2x m/s, which of the following statements are true, assuming a max deceleration?
I: The stopping time is doubled

II: The stopping distance is doubled

III: The stopping distance is quadrupled

Answer 35

I and III are true

According to the formula v² = v_o² + 2ad, the initial velocity, v_o, can be related to the stopping distance, d. If v is zero, and the equation is rearranged for d, it becomes d = v_o²/2a. Therefore, if v_o is doubled, the stopping distance, d, is quadrupled.

To determine the relationship between v_o and t, it becomes t = -v_o/a. Therefore, if v is doubled, the stopping time, t, is doubled.

Question 36

An object is thrown with an initial speed of 7m/s directed 45º above the horizontal from a cliff. After reaching the peak of its trajectory, it falls 20m to the ground below. What is the approximate ratio of time it takes to hit the ground from the peak of the trajectory to the time it takes from its release to the peak of the trajectory?

A) 0.5

B) 1

C) 2

D) 4

Answer 36

D) 4

To calculate the time it takes for the object to hit the ground from the peak, use d = v_ot + 1/2at² → 0 + 1/2(10)t² → 20 = 5t² → t = 2s

To calculate the time it takes to reach the peak, use v = v_o + at → 0 = 7sin45 - 10t. → 10t = 5 → t = 0.5s

So, the ratio of the time it takes to hit the ground from its peak to the time it takes to reach the peak is 2/0.5 = 4

Question 37

Neglecting air resistance, what is the total velocity of a parachutist just before engaging his parachute, 8s after dropping from an airplane flying horizontally at 60 m/s?

A) 60 m/s

B) 80 m/s

C) 100 m/s

D) 140 m/s

Answer 37

C) 100 m/s

To calculate the vertical component of velocity, use #2 of the big five: v_f=v_i + at. v_i is zero because the person is starting from rest vertically speaking. Using 10 m/s² for acceleration of gravity, you get 10m/s² x 8s = 80m/s.

Horizontal velocity remains the same throughout the drop since air resistance is negligable. Horizontal velocity = 60m/s

You do not add the 2 numbers. You add their vectors. Their vectors is proportional to a 3-4-5 triangle multiplied by 20. 5 x 20 = 100m/s