A particle travelling along a straight line travels the first 50 m with a uniform velocity of 5

step 1 Let us solve the first part of this problem where we need to calculate the average velocity. The

A particle travelling along a straight line travels the...

A particle travelling along a straight line travels the first $50 \mathrm{~m}$ with a uniform velocity of $5 \mathrm{~m} \mathrm{~s}^{-1}$, travels at a uniform velocity of $8 \mathrm{~m} \mathrm{~s}^{-1}$ for the next $5 \mathrm{~s}$ and travels at a uniform velocity of $12 \mathrm{~m} \mathrm{~s}^{-1}$ for the next $10 \mathrm{~s}$. (i) What is the average velocity of the journey? (ii) If the last part of the journey (during last $10 \mathrm{~s}$ ), was performed at a constant acceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$ from an initial velocity of $8 \mathrm{~m} \mathrm{~s}^{-1}$, what is the average velocity of the journey?

A particle travelling along a straight line travels the first $50 \mathrm{~m}$ with a uniform velocity of $5 \mathrm{~m} \mathrm{~s}^{-1}$, travels at a uniform velocity of $8 \mathrm{~m} \mathrm{~s}^{-1}$ for the next $5 \mathrm{~s}$ and travels at a uniform velocity of $12 \mathrm{~m} \mathrm{~s}^{-1}$ for the next $10 \mathrm{~s}$.
(i) What is the average velocity of the journey?
(ii) If the last part of the journey (during last $10 \mathrm{~s}$ ), was performed at a constant acceleration of $2 \mathrm{~m} \mathrm{~s}^{-2}$ from an initial velocity of $8 \mathrm{~m} \mathrm{~s}^{-1}$, what is the average velocity of the journey?

Key Concepts

Kinematic Equations

Kinematic equations are a set of formulas used to describe the motion of objects under constant acceleration. They link displacement, initial velocity, acceleration, time, and final velocity, and provide a mathematical framework to analyze and compute the results of motion segments where acceleration is a factor. These equations are critical tools for solving problems involving changes in velocity over time.

Constant Acceleration

Constant acceleration describes a situation where an object’s velocity changes at a constant rate over time. In such cases, kinematic equations are applicable to determine various parameters such as displacement, final velocity, and time. This concept is key when dealing with parts of a journey where the speed is not constant but changes steadily according to a given acceleration value.

Uniform (Constant) Motion

Uniform motion refers to movement with a constant velocity, meaning that both the speed and the direction of the object remain unchanged. In problems involving uniform motion, calculations are simplified since the displacement during any time interval is just the product of the constant speed and the time interval. This concept is essential for segments of a journey that are traveled at a fixed velocity.

Average Velocity

Average velocity is defined as the total displacement divided by the total time taken. It is a measure of the overall rate at which an object covers distance, regardless of the variations in speed during different segments of its journey. This concept is used to give a single value that describes the motion over a period of time, combining segments with different speeds or acceleration conditions.

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