Kinematics and motion in two dimensions

​Vectors- motion in two directions

​Motion in two dimensions consists of horizontal and vertical components.

Understand the independence of horizontal and vertical vectors in two-dimensional motion.

​Motion in a plane is also referred to as a motion in two dimensions. For example – Circular Motion, Projectile Motion, etc. For the analysis of such type of motion (i.e. Projectile Motion), the reference point will be made of an origin and the two coordinate axes X and Y. One of the most common examples of motion in a plane is Projectile motion.

​These are the equations used to solve kinematic problems. Copy them to your equation card.

Multiple Choice

If a ball is thrown up and lands at the same location, what was its acceleration?

• -10 m/s² on the way up and +10 m/s² on the way down.

• -10 m/s² the entire time.

• +10 m/s² on the way up and -10 m/s² on the way down.

Multiple Choice

Free fall is

• moving through the air under the influence of the force of gravity only.

• not paying for a fall.

• clothing sale with lots of orange & brown clothes.

• a feather dropped from an airplane.

Multiple Choice

A textbook is dropped from a second floor window and falls to the ground. What happens to the acceleration as the book falls to the ground

• the acceleration increases

• the acceleration decreases

• the acceleration remains constant

Multiple Choice

The state that exists when the only force acting on an object is gravity is called

• free fall

• inertia

• acceleration

• momentum

Multiple Choice

Heavier objects free fall faster than lighter objects.(in the absence of the air resistance)

• True

• False

Multiple Choice

Do free falling objects move at constant velocity or do they accelerate?

• Falling objects accelerate at -9.8 m/s²
• Falling object move at constant velocity
• Falling objects accelerate at 100 m/s²
• It depends on the mass: heavy objects accelerate, light objects do not

Multiple Choice

Which would hit the ground first if dropped from the same height in a vacuum—a feather or a metal bolt?

• the feather
• the metal bolt
• They would hit the ground at the same time.
• They would be suspended in a vacuum.

Multiple Choice

When there is no air resistance, objects of different masses dropped from rest

• fall with equal accelerations and with equal displacements.
• fall with different accelerations and with different displacements.
• fall with equal accelerations and with different displacements.
• fall with different accelerations and with equal displacements.

Multiple Choice

Which would fall with greater acceleration in a vacuum—a leaf or a stone?

• the leaf
• the stone
• They would accelerate at the same rate.
• It is difficult to determine without more information.

Multiple Choice

In a normal environment, why does a bowling ball and feather hit the ground at different times when dropped from the same height?

• They don't; they hit the ground at the same time.
• One is more dense than the other.
• One is heavier than the other.
• Air resistance 

Multiple Choice

What is the velocity of a ball that has been dropped off a cliff after 1 , 2, 3, 4, and 5 seconds? (assume g is rounded to 10 m/s²)?. 

• 10, 20, 30, 40, 50 m/s
• 5, 10, 15, 20, 25 m/s
• 5, 20, 45, 80,125 m
• 10,10,10,10,10 m/s

Multiple Choice

If you throw a baseball straight up, what is its velocity at the highest point?

• 9.8 m/s²
• 9.8 m/s
• 0 m/s²
• 0 m/s

Multiple Choice

At what point is v_y= 0 m/s?

• A

• B

• C

• D

• None of these points

Multiple Choice

If you throw a baseball straight up, what is its acceleration at the highest point?

• -9.8 m/s²
• -9.8 m/s
• 0 m/s²
• 0 m/s

Multiple Choice

The more mass an object has, the faster it will fall.

• True
• False

Multiple Choice

If I throw a crayon straight up at 12m/s, how fast is its speed when i catch it at the same height?

• -6 m/s
• -12 m/s
• -18 m/s
• -24 m/s

Multiple Choice

What is the horizontal acceleration of a projectile?

• 0 m/s²
• -9.8 m/s²

Multiple Choice

Velocity is different from speed in that velocity is speed in a given direction.

• True
• False

Multiple Choice

What is the displacement from 2 to 10 seconds?

• 64 km
• 100 m
• 64m 
• 32 m 

Multiple Choice

What are the components of this vector?

• South and East
• South and West
• North and East
• North and West

Multiple Choice

What is the resultant of these two vectors?

• +2a
• 0
• -2a
• +a

Multiple Choice

Consider drops of water leaking from a water faucet. As the drops fall they 

• remain at a relatively fixed distance from each other
• get farther apart
• get closer together

Multiple Choice

The path followed by a projectile is also known as its

• trajectory

• range

• height

• vertical displacement

Multiple Choice

What is the direction of the acceleration for any projectile?

• The direction the projectile is traveling.

• Down

• Up

• Sideways

Multiple Choice

What is the acceleration of a projectile?

• 0 m/s²
• 9.8 m/s²

Multiple Choice

At what point can we measure the maximum height?

• A

• B

• C

• D

• None of these points

Multiple Choice

At which point can we measure the maximum range of the projectile? (it's landing point)

• A

• C

• D

• E

Multiple Choice

At which point is the velocity of the object the same as the initial velocity at A?

• A

• C

• D

• E

Multiple Choice

At which point could you measure half the time the projectile is in the air?

• A

• C

• D

• E

Multiple Choice

At which point is our object slowing down?

• B

• D

• E

• All points

Multiple Choice

At which of the following places does a projectile have the greatest acceleration?

• At the peak of its trajectory

• Half way to the peak

• At the instant it is launched

• All points have the same acceleration

Multiple Choice

A boat travels 12.0 m while it reduces its velocity from 9.5 m/s to 5.5 m/s. What is the magnitude of the boat’s acceleration while it travels the 12.0 m?

• 1.3 m/s²
• 2.5 m/s²
• 3.0 m/s²
• 7.5 m/s²

Multiple Choice

Kinematic equation can only be used when you have a constant ....

• Position

• Velocity

• Acceleration

• Time

Multiple Choice

The unit we use to measure acceleration is ___.

• m/s

• m

• s

• m/s²

Multiple Choice

A ball is dropped from a building. How fast is it traveling after falling for 1.77 s? (Hint: It's a free falling object)

• 14.76 m/s

• 17.35 m/s

• 18.91 m/s

• 20.03 m/s

Multiple Choice

A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car. Choose the appropriate equation.

• v=v_o+at

• d=v_ot+1/2at²

• v²=v_o²+2ad

• d=1/2(v+v_o)t

Multiple Choice

Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of 444 m/s in 1.83 seconds, then what is the distance that the sled travels?

Choose the appropriate equation.

• v=v_o+at

• d=v_ot+1/2at²

• v²=v_o²+2ad

• d=1/2(v+v_o)t

Multiple Choice

If Michael Jordan has a vertical leap of 1.29 m, then what is his takeoff speed if his acceleration is -9.8 m/s² and his velocity at the top of his leap i 0 m/s?

• v=v_o+at

• d=v_ot+1/2at²

• v²=v_o²+2ad

• d=1/2(v+v_o)t

Multiple Choice

An engineer is designing the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate is likely to be 3 m/s². The takeoff speed for this plane will be 65 m/s. All airplanes will start from rest. Assuming this minimum acceleration, what is the minimum allowed length for the runway?

• v=v_o+at

• d=v_ot+1/2at²

• v²=v_o²+2ad

• d=1/2(v+v_o)t

Multiple Choice

The unit we use to measure speed is ___.

• m/s

• m

• s

• m/s²

Multiple Choice

The unit we use to measure distance is ___.

• m/s

• m

• s

• m/s²

Multiple Choice

The unit we use to measure time is ___.

• m/s

• m

• s

• m/s²

Multiple Choice

Which of the following symbols represent speed when time is zero?

• v

• v₀

• a

• x

Multiple Choice

Which of the following symbols represent speed at any time?

• v

• v₀

• a

• x

Multiple Choice

What does g represent as in physics

• greg

• gravity

• gas

• Grover

Multiple Choice

What is the symbol for distance?

• m

• M

• d

• D

Multiple Choice

What is the symbol for position?

• p

• Ƥ

• x

• y

Multiple Choice

What is the symbol for height?

• hT

• Y

• Ht

• y

Multiple Choice

What is the Symbol for force?

• F

• ḟ

• N

• Fx

Multiple Choice

What is the Formula for Speed?

• v = d/t

• s = t/d

• Speed = V_i - V_f

• 100mph

Multiple Choice

The symbol Δ, stands for a ______________

• pyramid

• total

• change in

• position

Multiple Choice

a = Δv / Δt

This is the formula to solve what?

• amplitude

• angular momentum

• Acceleration

• Delta change

Multiple Choice

What is the force of Gravity?

• Down

• 1g

• 9.8 m/s²

• 8.9 m/s²

Explanation Slide...

Force = mass x acceleration

Multiple Choice

What is the formula to find Force

• F= d/t

• m/a = F

• F = mA

• F= ma

Explanation Slide...

You can run 5 miles and have a displacement of 0. Displacement is how far you displace from where you started.

Multiple Choice

A change in position of an object is called ____________.

• distance

• displacement

• magnitude

• separation

Explanation Slide...

acceleration units are always m/s2 or m/s/s

Multiple Choice

If a 73.2kg object is receiving a net force of 933N to the West, then what will be its acceleration?

• 12.74a²

• 12.74 m/s

• 12.74 m/s²

• 12.74

Explanation Slide...

F = mass x acceleration is the same asF = mass x (∆v /∆t)Because acceleration = (∆v /∆t)

Multiple Choice

What things are needed to find force (F)?

• mass and velocity

• mass and final velocity

• momentum and acceleration

• mass, ∆v and ∆t

Multiple Choice

This is the formula for ______________________________.

• amplitude

• Velocity

• Acceleration

• V₀

Multiple Choice

This is the formula for____

• going fast

• speed

• displacement

• Velocity

Multiple Choice

What does V_{f represent?}

• vector function

• velocity forward

• final velocity

• initial velocity

Multiple Choice

How long would it take a car, starting from rest and accelerating uniformly in a straight line at 5 m/s², to cover a distance of 200 m?

• 9.0s

• 10.5s

• 12.0s

• 15.5s

Multiple Choice

Sam jumped from a plane. His acceleration was 10m/s². He hit the ground in 8 seconds. What was his velocity just before he hit the ground?

• 300 m/s

• 30 m/s

• 320 m/s

• 80 m/s

Multiple Choice

The speed of an object undergoing constant acceleration increases from 8.0 m/s to 16.0 m/s in 4 s. What is the acceleration of the object?

• 8 m/s²

• 4 m/s²

• 2 m/s²

• 1 m/s²

Multiple Choice

A car accelerates uniformly from rest at 10 m/s². How long does it take the car to travel a distance of 125 meters?

• 2 seconds

• 3 seconds

• 4 seconds

• 5 seconds

Multiple Choice

A toy car is given an initial velocity of 4 m/s and experiences a constant acceleration of 6 m/s². What is the final velocity after 5 seconds?

• 24 m/s

• 10 m/s

• 34 m/s

• 6 m/s

Multiple Choice

A car starts from rest and after 7 seconds it is moving at 42 m/s. What is the car’s acceleration?

• 0.17 m/s²

• 1.67 m/s²

• 6 m/s²

• 7 m/s²

Multiple Choice

What's the missing part in the given kinematic equation?

$$x\ =\ x_i\ +\ v_i\ \times t\ +\ \frac{1}{2}\left(a\right)\left(-\right)$$  

• $$t$$  

•   $$t^2$$  

• $$v_f$$  

• Δv

Multiple Choice

What is the rate of acceleration of a mountain bike if it slows down from 9.4 m/s to 3.0 m/s in a time of 3.75 s?

a = vf – vi / t

• -0.61 m/s²

• -1.71 m/s²

• -1.19 m/s²

• -2.07 m/s²

Multiple Choice

A policeman traveling 19.5 m/s spots a speeder ahead, so he accelerates his vehicle at a steady rate of 1.81 m/s² for 3.2 s, at which time he catches up with the speeder. What distance does the police car cover in that time?

d = v_it + ½ at²

• 35.98 m

• 56.32 m

• 71.67 m

• 91.02 m

Multiple Choice

A car parked on a hill starts to coast down the hill, accelerating from rest at a constant rate of 0.45 m/s². How fast will the car be moving after 7.0 s?

v_f = v_i + at

• 3.15 m/s

• 5.07 m/s

• 6.97.15 m/s

• 7.81 m/s

Multiple Choice

An airplane accelerates down a runway from rest at 3.98 m/s² for 25.9 s until it lifts off the ground. Determine the distance traveled before takeoff.

d = v_it + ½ at²

• 934.0 m

• 1004.7 m

• 1184 m

• 1334.9 m

Multiple Choice

A ball is dropped from a building. How fast is it traveling after falling for 1.77 s?

v_f = v_i + at

• 14.76 m/s

• 17.35 m/s

• 18.91 m/s

• 20.03 m/s