Physics Chapter: Uniformly Accelerated Motion

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Questions and Answers

What does the slope of a position-time graph indicate in uniformly accelerated motion?

The acceleration of the object

The displacement of the object

The average velocity of the object

The instantaneous velocity of the object (correct)

Which equation represents the position-time relation for uniformly accelerated motion?

s = vot + 1/2at^2 (correct)

s = vt

s = 1/2at + b

s = vt^2

What does the area under the curve on an acceleration-time graph represent?

Change in velocity (correct)

Total distance traveled

Final acceleration

Initial velocity

What kind of curve is the position-time graph for uniformly accelerated motion?

A parabola Signup and view all the answers

How would the acceleration-time graph appear for uniformly accelerated motion?

A straight line parallel to the time axis Signup and view all the answers

What is the purpose of drawing a tangent line on a curved position-time graph?

To find the instantaneous velocity at a particular point Signup and view all the answers

Which of the following statements about the position-time graph is true for uniformly accelerated motion?

The slope varies and indicates changing velocity Signup and view all the answers

In the context of motion, what does the slope of a velocity-time graph indicate?

Acceleration Signup and view all the answers

Which of the following accurately describes the position-time graph for uniformly accelerated motion?

An ascending curve Signup and view all the answers

Which graph should you expect when observing the velocity-time relationship in uniformly accelerated motion?

A linear graph indicating changing velocity Signup and view all the answers

When a car accelerates from rest at a constant rate of 2.0 m/s², how long will it take to cross a 25.0 m wide intersection?

5 seconds Signup and view all the answers

Instantaneous acceleration can be distinguished from average acceleration by:

Finding the slope of the tangent line to the velocity-time graph at a specific point Signup and view all the answers

Which of the following describes the relationship between time and position in the position-time graph of uniformly accelerated motion?

Quadratic relationship with a variable slope Signup and view all the answers

What is the relationship between uniform motion and uniformly accelerated motion?

Uniform motion has a constant velocity while uniformly accelerated motion has changing velocity. Signup and view all the answers

What is the defining characteristic of a velocity-time graph for uniform motion?

A horizontal straight line Signup and view all the answers

Which statement best describes the motion of a particle with zero acceleration?

The particle is moving at constant speed. Signup and view all the answers

What does the slope of the tangent line to a position-time graph represent?

Instantaneous velocity of the object Signup and view all the answers

What is represented by the area under a velocity-time graph?

The total displacement of the object Signup and view all the answers

Which of the following describes the velocity-time graph for an object under uniform acceleration?

A straight line inclined to the time axis Signup and view all the answers

How is instantaneous velocity calculated from a position-time graph at a given time?

By finding the slope of the tangent line at that point Signup and view all the answers

What happens to the velocity-time graph when a particle undergoes uniform retardation?

It becomes a straight line with a negative slope Signup and view all the answers

If a particle starts from rest and accelerates uniformly, how would its position-time graph appear?

A curve that is concave upwards Signup and view all the answers

Which of the following equations relates to the area under a velocity-time graph for an object with uniform acceleration?

$v_0 t + rac{1}{2} a t^2$ Signup and view all the answers

What is the main purpose of the slope in a v-t graph?

To indicate the change in velocity over time Signup and view all the answers

If an object's acceleration is zero, what can be inferred about its velocity-time graph?

It is a horizontal line Signup and view all the answers

Which statement about instantaneous velocity is true?

It varies continuously along a position-time graph Signup and view all the answers

Which aspect of motion can be retrieved directly from the slope of a velocity-time graph?

Accurate representation of time intervals Signup and view all the answers

When a particle is moving with variable velocity, how is its velocity-time graph typically characterized?

An irregular shape with ups and downs Signup and view all the answers

During non-uniform motion, how does the displacement relate to the area under the velocity-time curve?

It may be less than or greater than the area under the curve Signup and view all the answers

What is the effect of a particle's initial velocity on its velocity-time graph?

It establishes the starting point along the velocity axis Signup and view all the answers

Study Notes

Uniformly Accelerated Motion Graphs

Position-time graphs for uniformly accelerated motion are parabolic, showing a quadratic relationship between position (s) and time (t). The equation for this relationship is s = vot + 0.5at².
The slope of the tangent to a position-time graph at any point represents the instantaneous velocity at that time. A tangent is a line that touches the curve at only one point and has the same slope as the curve at that point.
Instantaneous velocity is the velocity of an object at a specific moment, calculated as the slope of the tangent to the position-time graph at that moment.
Example: A car accelerating at 10 m/s² from rest for 10 seconds: the position-time graph is plotted by calculating positions for various times using s = 0.5at², and the instantaneous velocity at 6 seconds is calculated by finding the slope of the tangent to the curve at t=6s.

Velocity-Time Graphs

Velocity-time graphs for uniformly accelerated motion are straight lines.
- If the initial velocity is zero, the line passes through the origin.
- If the initial velocity is not zero, the line starts above or below the origin, depending on whether the initial velocity is positive or negative. The y-intercept is the initial velocity (v₀), and the slope of the line represents the acceleration (a).
The area under a velocity-time graph represents the displacement of the object during the corresponding time interval. This area is calculated as the area of the rectangle plus the area of the triangle beneath the line.
Example: A truck accelerating from rest at 20.0 m/s² for 5 seconds — the position-time graph is plotted by calculating positions for various times using the area under the velocity-time curve.
The slope of a velocity-time graph is equal to the acceleration of the object.
If velocity decreases uniformly (retardation or deceleration). the velocity-time graph is a straight line with a negative slope. If the object stops, this line touches/intersects the time axis.
For non-uniform motion, the velocity-time graph is irregular.

Acceleration-Time Graphs

Acceleration-time graphs for uniformly accelerated motion are horizontal straight lines.
The acceleration is constant, which makes acceleration-time graphs a horizontal straight line.
The area under an acceleration-time graph represents a change in velocity over the plotted time interval.

Key Concepts

The slope of a position-time graph gives the instantaneous velocity.
The area under a velocity-time graph gives the displacement.
The slope of a velocity-time graph gives the acceleration.

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Description

Explore the characteristics of position-time and velocity-time graphs in uniformly accelerated motion. Understand how to interpret the slope of the tangent and calculate instantaneous velocity using the provided equations. Test your knowledge on plotting and analyzing these essential graphs in physics.