Mada za sehemu hiiMotion In Straight LineMada 5
Acceleration is the rate of change of velocity. It refers to how much the velocity of an object changes per unit time. When an object speeds up, slows down, or changes direction, it experiences acceleration. Acceleration is a vector quantity, which means it has both magnitude and direction.
Mathematically, acceleration can be expressed as:
Where:
v = final velocity (in meters per second, m/s)
u = initial velocity (in meters per second, m/s)
t = time taken for the change in velocity (in seconds, s)
The formula expresses acceleration a as the change in velocity divided by the time taken to experience that change. The change in velocity is represented by the difference between the final velocity v and the initial velocity u.
Initial Velocity (u): The velocity of the object at the start of the observation period.
Final Velocity (v): The velocity of the object at the end of the observation period.
Time (t): The time interval over which the change in velocity occurs.
If a car increases its speed from 10 m/s to 30 m/s in 5 seconds, the acceleration can be calculated as:
This means the car's velocity increased by 4 meters per second every second.
Acceleration is measured in meters per second squared (m/s²) in the International System of Units (SI).
- Positive Acceleration: When an object speeds up, resulting in a positive acceleration.
- Negative Acceleration (Deceleration): When an object slows down, resulting in a negative acceleration.
- Zero Acceleration: When an object moves at a constant velocity, there is no change in velocity, and thus the acceleration is zero.
Acceleration plays a crucial role in understanding the motion of objects and is essential in the study of dynamics in physics.
Interpret velocity time-graph
This is velocity against time graph. Consider a body accelerating uniformly from rest to a certain velocity v within time t. This can be represented graphically as shown below.
The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. If the acceleration is zero, then the slope is zero (i.e., a horizontal line). If the acceleration is positive, then the slope is positive (i.e., an upward sloping line).
The distance x moved by the body is given by the area under the velocity-time curve. In this case, the area of the triangle OBC represents the distance.
A car starts from rest and accelerates to a velocity of 120 m/s in one minute. It then moves with this speed for 40 seconds, finally decelerates to rest after another 2 minutes. Calculate the:
The distance travelled
The total time taken for the whole motion
The deceleration
The average velocity
Solution
1st Stage: Acceleration
Initial velocity: u = 0 m/s
Final velocity: v = 120 m/s
Time: t₁ = 1 min = 60 s
We can calculate the distance traveled during the acceleration phase using the formula:
Substitute the values:
2nd Stage: Uniform Velocity
Initial velocity: u = v = 120 m/s
Time: t₂ = 40 s
We can calculate the distance traveled during the uniform velocity phase using the formula:
Substitute the values:
3rd Stage: Deceleration
Initial velocity: u = 120 m/s
Final velocity: v = 0 m/s
Time: t₃ = 2 min = 120 s
We can calculate the distance traveled during the deceleration phase using the formula:
Substitute the values:
Total Distance Traveled
The total distance traveled is the sum of the distances from all three stages:
Total Time Taken
The total time taken is the sum of the times for each stage:
Deceleration
Using the equation for velocity:
Substitute the values:
Solve for a:
Average Velocity
The average velocity is calculated as the total distance traveled divided by the total time taken:
Total Distance Traveled: 15600 m
Total Time Taken: 220 s
Deceleration: 2 m/s²
Average Velocity: 71 m/s
Deceleration, also known as retardation, is the rate of decrease of velocity. It refers to the decrease in velocity of an object per unit of time. Mathematically, it can be expressed as:
Where:
v is the final velocity
u is the initial velocity
t is the time taken for the change in velocity
Uniform acceleration or retardation occurs when the rate of change of velocity (either increasing or decreasing) remains constant. This means that the object's velocity either increases or decreases at a constant rate over time. Mathematically, if the acceleration is constant, the change in velocity per unit time remains the same throughout the motion of the object.
Important notes:
- When a body starts from rest: The velocity of the body is zero at the start, meaning u = 0. If the body starts from rest and moves under constant acceleration, its velocity increases over time.
- When a body is brought to rest: The final velocity of the body becomes zero, i.e., v = 0, and it comes to a stop due to negative acceleration (retardation).
- When the velocity of a body is constant: The acceleration is zero because there is no change in velocity over time.
- When the velocity of a moving object increases: The acceleration becomes positive because the object is gaining speed.
- When the velocity of a moving object decreases: The acceleration becomes negative, known as retardation. This negative acceleration indicates that the object is slowing down or coming to a stop.
Example:
If a car moves at a speed of 30 m/s and decelerates to rest in 10 seconds, we can calculate the retardation:
Initial velocity: u = 30 m/s
Final velocity: v = 0 m/s
Time taken: t = 10 s
Using the formula for deceleration:
The negative sign indicates that this is a deceleration (retardation).
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