Scalars and Vectors
Fastest=3, 1, 2=slowest.
At t=0, an object has a velocity of 1m/s. At time 6, it has a velocity of 3m/s. What is the average acceleration between t=0 and t=6?
If an object has a velocity vs. time graph that looks like a straight horizontal line, what will the acceleration vs. time graph look like? Draw on your desk.
A straight horizontal line on the x axis (a=0m/s/s)
If I throw a ball straight upwards at 10m/s, how long will it take to reach max height?
1 second
Who is Madi's favorite student?
I love them all equally.
An object is initially at the origin. The object changes its position to the right by 4 units. The object the changes its position to the left by 3 units. Indicate the magnitude of the object’s change in position and provide a valid justification.
1 unit, because in one dimension vectors with opposite directions have opposite signs. The total displacement is equal to the vector sum of the two displacement vectors.
A 1.5 kg cart starts from rest and then accelerates at a constant rate of 2 m/s/s to the right for 5 s. What is the displacement of the cart during this time?
∆x=1/2at2+v0t
∆x=(1/2)(2)(52)+0
∆x=25m
A position vs time graph shows an object traveling in the negative direction slowing down. Sketch the graph.
Should look like the left half of someone's smile (someone you are looking straight ahead at)
3.58s
Who is Madi's favorite student, really?
Honestly, it changes day to day.
During time interval Δt1, a car starts from rest and speeds up at a constant rate to the right until reaching a final velocity vf. Then, during time interval Δt2 the car slows down at a constant rate until it comes to rest. Correctly indicate whether the signs and directions of the car’s acceleration during the two time intervals are the same or different.
Signs and direction of acceleration are different. Because signs are used to indicate direction, they correspond with each other.
A cart is moving along a straight track and has velocity +0.5 m/s and positive acceleration at time 1 s. At
time 3 s, the cart reaches a maximum speed. At time 4 s, the cart again has velocity +0.5 m/s, but with negative acceleration. A student claims that the average acceleration of the cart between time 1 s and 4s time is zero. Is the student’s claim correct? Why or why not?
Yes, because the final velocity of the cart is equal to the initial velocity.
I launch a projectile at 45 degrees above the horizontal. Sketch a velocity vs. time graph for the horizontal direction.
Should look like a straight line above the x-axis.
If a projectile is launched at an angle of 60 degrees above horizontal at 40m/s, what is the initial velocity in the vertical direction?
34.64m/s
Who is Madi's favorite student today?
Today, Julieta.
Vectors A and B are parallel to the x-axis. Vector C is the defined as the sum of Vectors A and B. Vector C has the same direction as Vector B. Vector B has a greater MAGNITUDE than Vector C.
What is the relationship between the magnitudes and directions of Vector A and B?
The magnitude of Vector A is less than Vector B, and their directions are opposite.
Three carts are free to move left or right on a horizontal track. Each cart experiences a constant acceleration. The initial and final velocities of each cart are indicated in the table. Which cart, if any, has a leftward acceleration?
Cart: (v0,vf)
Cart 1: (30 cm/s to the right, 20 cm/s to the right)
Cart 2: (30 cm/s to the left, 20 cm/s to the left)
Cart 3: (10cm/s to the left, 10 cm/s to the right)
Cart 1
On Planet Y, the position of a ball falling from rest with respect to time (with negligible air resistance) can be modeled by the equation position=3.2t2. How does gravitational acceleration on Planet Y compare to Earth?
gEarth= 1.5 • gPlanet Y
0.65gEarth=gPlanet Y
A boulder rolls off of a 50m cliff horizontally at 5m/s. How long does it take to reach the bottom?
(Square root of 10) t=3.16s
Who is Madi's favorite student tomorrow?
Tomorrow, Felipe.
Vectors M and N are parallel to the x-axis. Let a= the absolute value of (M +N) and let b= the absolute value of M + the absolute value of N. A student claims it is possible that a<b. Is this claim correct? Provide a justification.
The claim is correct, because the vectors M and N could be in opposite directions.
Two cars pass by each other on a straight road. Car 1 has a speed v0 to the right and Car 2 has the same speed to the left. Immediately after passing each other, both cars experience a constant acceleration a0 directed to the left. At the instant Car 1 comes to rest, what is the speed v2 of Car 2?
v2 = 2v0
A ball is thrown straight up. Sketch a position vs. time, a velocity vs. time, and acceleration vs. time graph for the ball's vertical motion. (General shape is ok)
Position vs. time= upside down parabola
Velocity vs. time= Straight line, y-intercept above x-axis, negative slope (-10 specifically)
Acceleration vs. time= Straight line at a=-10.
A boulder rolls off of a 50m cliff horizontally at 5m/s. How far away from the base of the cliff does it land?
3.16*5=15.81m
Who is Madi's favorite student on Friday?
Possibly, Cris. If he aces the FRQ section on the progress check.