True or False? You can assume that the answer to a two-dimensional constant-acceleration question is a vector.

False. It depends on what has been asked for. Speed and distance are scalars, so those answers are single numbers, found by taking the magnitude of the relevant vector. A question asking for the distance of a particle from its starting point wants the magnitude of the displacement, not the displacement itself.

A LevelMathsEdexcelMechanicsFlashcardsKinematicsConstant Acceleration in 2D

Constant Acceleration in 2D (Edexcel A Level Maths: Mechanics): Flashcards

Exam code: 9MA0

1/6

0Still learning

Know0

Frontsuvat in 2D
Which of the five constant-acceleration formulae cannot be written in vector form, and what do you do instead?

Was this flashcard helpful?

Cards in this collection (6)

Which of the five constant-acceleration formulae cannot be written in vector form, and what do you do instead?
The formula that cannot be written in vector form is $v^{2} = u^{2} + 2 a s$ , because squaring a vector has no meaning here.
Instead, apply it to each direction separately: one ordinary equation in numbers using only the $i$ components, and one using only the $j$ components.
The other four formulae do work in vector form, because they only add vectors and multiply them by the scalar $t$ .
In two dimensions the constant-acceleration formulae are written with vectors. Fill in the blanks:
$s =______t + \frac{1}{2}______t^{2}$
The completed formula is:
$s = u t + \frac{1}{2} a t^{2}$
The displacement, the initial velocity and the acceleration are all vectors, which is why they are written in bold. Time is a scalar and is not.
In a two-dimensional constant-acceleration problem, what are the two ways of setting up the working?
Either work with one vector equation, keeping the vectors in component form all the way through, or split it into two separate equations, one for the $i$ components and one for the $j$ components, and solve those independently.
Both are valid because a vector equation holds exactly when it holds in each direction separately.
Time is a scalar, so it appears unchanged in either approach.
A question says a particle is travelling parallel to the vector $i$ . What does that tell you about its velocity?
Its velocity is a scalar multiple of $i$ , so the $j$ component of the velocity is zero.
More generally, travelling parallel to a given vector means the velocity is that vector multiplied by some number. That is enough to write the whole velocity in terms of a single unknown, even when no components have been given.
Why can "find the acceleration" be ambiguous in two dimensions, when "find the velocity" is not?
Velocity has a separate word for its magnitude, speed, and displacement has one too, distance, but acceleration has no such word: the same word is used for the vector and for its magnitude.
So "find the acceleration" may want the vector, in component form, or its magnitude, which is a single number.
The wording decides it: an answer asked for "in the form $(a i + b j)$ " is the vector.
True or False?
You can assume that the answer to a two-dimensional constant-acceleration question is a vector.
False.
It depends on what has been asked for. Speed and distance are scalars, so those answers are single numbers, found by taking the magnitude of the relevant vector.
A question asking for the distance of a particle from its starting point wants the magnitude of the displacement, not the displacement itself.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:Variable Acceleration in 2DNext:Projectiles