# Some quick questions concerning uniform acceleration and linear motion

• Ellio
In summary, when calculating acceleration, both acceleration and speed should be in consistent units. Additionally, to find the total distance an object has traveled, one must use the area under a graph of velocity against time, taking into consideration the shape of the graph. The formula for displacement varies depending on the shape of the graph, with the simplest being x(t) = x0 + v × (t-t0) and more complex shapes requiring the use of x(t) = x0 + v × (t-t0) + 1/2 × a × (t-t0).
Ellio
Homework Statement
just general questions
Relevant Equations
x(t) = x0 + v × (t-t0)
x(t) = x0 + v × (t-t0) + 1/2 × a × (t-t0)
Hello, I hope you are all having a great day !
I've got a physics test in a couple of days and I have some questions:1.
In a calculation, if the acceleration is in m/s², I presume the speed also has to be in m/s and not in km/h ?

2.

So with this graph (v with t), I have to find the total distance the object made.
The movement is at start an uniform acceleration then a linear motion and it finishes with an uniform acceleration again.
I have to find the total distance by doing v × t = x
But i thought this was just with linear motion (v = x/t)I hope the question were clear, I apologise if they weren't. Thank you in advance !

1. Yes. You must use consistent units.

2. Displacement is area under a graph of velocity against time. You need to calculate this according to the shape of the graph: rectangles, triangles or other shapes. ##A = vt## only applies for a rectangle, where ##v## represents the constant velocity.

Ellio said:
Homework Equations: x(t) = x0 + v × (t-t0)
x(t) = x0 + v × (t-t0) + 1/2 × a × (t-t0)
Note that the latter equation should be $$x(t) = x_0 + v(t-t_0) + \frac{1}{2}a(t-t_0)^2$$

## 1. What is uniform acceleration?

Uniform acceleration is when an object's velocity changes by an equal amount in each unit of time.

## 2. What is linear motion?

Linear motion is when an object moves in a straight line at a constant speed and direction.

## 3. How can uniform acceleration be calculated?

Uniform acceleration can be calculated using the formula a = (vf - vi) / t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time taken.

## 4. Can an object have uniform acceleration and linear motion at the same time?

Yes, an object can have uniform acceleration and linear motion at the same time if its velocity is changing at a constant rate while moving in a straight line.

## 5. What is the difference between uniform acceleration and constant velocity?

Uniform acceleration involves a change in velocity over time, while constant velocity means the object's speed and direction remain the same. In other words, uniform acceleration is a type of non-constant velocity.

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