1.5 The Kinematics Equations Flashcards
What is the formula for the area of a trapezoid?
A = (b1 + b2) / 2 * h
b1 and b2 are the lengths of the parallel sides, and h is the height.
How do you calculate displacement from a velocity-time graph?
Use the area under the curve of the graph
Displacement can be calculated as the area between the velocity curve and the time axis.
What is the equation derived from the area under the velocity-time graph?
d = Vave * At
d represents displacement, Vave is average velocity, and At is the time interval.
What does the variable ‘At’ represent in the equation d = Vave * At?
At represents the time interval
It is the duration over which the average velocity is calculated.
In the context of a velocity-time graph, what does the area under the graph represent?
Displacement
The area can be calculated using geometric methods depending on the shape under the curve.
True or False: The area under a velocity-time graph can be used to determine distance traveled.
True
Distance is the total displacement, considering the direction of motion.
What does the area under the velocity-time graph represent?
The equation d = Vave At
This equation is derived from the area under the velocity-time graph.
What is the second kinematics equation?
Ad = (V_i + V_f) At
In this equation, V_i is the initial velocity, V_f is the final velocity, and At is the time interval.
In the equation Ad = (V_i + V_f) At, what does At represent?
The time interval
At is the duration over which the velocities are averaged.
Fill in the blank: The second kinematics equation is Ad = _______.
(V_i + V_f) At
What does the area under the velocity-time graph represent?
The equation d = Vave At
This equation is derived from the area under the velocity-time graph.
What is the second kinematics equation?
Ad = (V_i + V_f) At
In this equation, V_i is the initial velocity, V_f is the final velocity, and At is the time interval.
In the equation Ad = (V_i + V_f) At, what does At represent?
The time interval
At is the duration over which the velocities are averaged.
Fill in the blank: The second kinematics equation is Ad = _______.
(V_i + V_f) At
How can you calculate the area under a velocity-time graph?
By considering it as a combination of a triangle and a rectangle.
What does the area of the rectangle under a velocity-time graph represent?
The displacement of an object traveling with a constant velocity.
What is the formula for the area of the rectangle in a velocity-time graph?
Area = V * Δt
What does the height of the rectangle represent in a velocity-time graph?
The constant velocity, V.
What does the base of the rectangle represent in a velocity-time graph?
The time interval, Δt.
What does the area of the triangle under a velocity-time graph represent?
The additional displacement resulting from the change in velocity.
What is the height of the triangle in a velocity-time graph?
ΔV = V - V₀
What is the base of the triangle in a velocity-time graph?
Δt.
What is the formula for the area of the triangle in a velocity-time graph?
Area = 0.5 * base * height
What is the final displacement formula combining both areas under the velocity-time graph?
Ad = V * Δt + 0.5 * ΔV * Δt.
Who achieved the fastest time of covering 1.6 km while flipping tiddly winks?
E. Wynn and Culliongham (UK).
What was the time taken to cover 1.6 km by E. Wynn and Culliongham?
52 minutes and 10 seconds.
What was the speed of E. Wynn and Culliongham during their record?
1.8 km/h.
True or False: The area under a velocity-time graph can only be a rectangle.
False.
Fill in the blank: The area of the triangle can be calculated as _______.
0.5 * Δt * ΔV.
What is the first step to obtain the fourth kinematics equation?
Derive the value of a required variable in one equation
After isolating V in the equation, what do you substitute it with?
Substitute v - GAt for v
What is the second equation used in the derivation process?
Ad = (V + v)At
What does the equation Ad = (V + v)At become after substitution?
Ad = (T - GAt + T)At
What is the result of simplifying the equation Ad = (T - GAt + T)At?
Ad = 2
Fill in the blank: To derive the fourth kinematics equation, you must _______.
[simplify the substituted equation]
Is the equation Ad = (V + v)At used in the process of obtaining the fourth kinematics equation?
True
What mathematical technique is used to derive the fifth kinematics equation?
Difference of squares
The difference of squares is expressed as (a + b)(a - b) = a² - b².
What is the isolated form of At in the equation a = ?
At = ?
The specific equation for acceleration (a) was not provided in the text.
What is the scalar form of the equation used for dividing vectors?
Ad = (v + v)At
This represents the scalar form of the kinematics equation.
How far did the tortoise cover at the National Tortoise Championships?
5.48 m
The tortoise set a world record on July 2, 1977.
What was the speed of the tortoise in km/h?
0.45 km/h
This speed was recorded during the championships.
What is the more standard form of the fifth kinematics equation?
v = y + 2aAd
This equation relates velocity, displacement, and acceleration.
Fill in the blank: The fifth kinematics equation involves the difference of ______.
squares
This refers to the mathematical technique used in deriving the equation.
What mathematical technique is used to derive the fifth kinematics equation?
Difference of squares
The difference of squares is expressed as (a + b)(a - b) = a² - b².
What is the isolated form of At in the equation a = ?
At = ?
The specific equation for acceleration (a) was not provided in the text.
What is the scalar form of the equation used for dividing vectors?
Ad = (v + v)At
This represents the scalar form of the kinematics equation.
How far did the tortoise cover at the National Tortoise Championships?
5.48 m
The tortoise set a world record on July 2, 1977.
What was the speed of the tortoise in km/h?
0.45 km/h
This speed was recorded during the championships.
What is the more standard form of the fifth kinematics equation?
v = y + 2aAd
This equation relates velocity, displacement, and acceleration.
Fill in the blank: The fifth kinematics equation involves the difference of ______.
squares
This refers to the mathematical technique used in deriving the equation.
