A particle had a speed of 18 m / s at a certain time, and 2.4 s later its speed was 30 m / s

step 1 In this question we have given an initial velocity that is V. V -Nor that is equals to 18 -meter

A particle had a speed of 18 m / s at a certain time, and...

A particle had a speed of $18 \mathrm{~m} / \mathrm{s}$ at a certain time, and $2.4 \mathrm{~s}$ later its speed was $30 \mathrm{~m} / \mathrm{s}$ in the opposite direction. What were the magnitude and direction of the average acceleration of the particle during this $2.4$ s interval?

Key Concepts

Average Acceleration

Average acceleration is defined as the change in velocity divided by the change in time. It quantifies how quickly the velocity of an object is changing and is itself a vector quantity, meaning it has both magnitude and direction.

Vector Quantities (Velocity and Acceleration)

Velocity and acceleration are vector quantities, which means they are described by both magnitude and direction. This concept is crucial when solving problems where direction changes, as positive and negative signs or specific directional adjectives are used to represent opposite directions.

Change in Velocity

The change in velocity is the difference between the final velocity and the initial velocity. When dealing with vector quantities, this involves taking into account the direction of each velocity. Accurate calculation of this change is essential for correctly determining the average acceleration.

Time Interval

The time interval is the period during which the change in velocity occurs. Dividing the overall change in velocity by this interval gives the average acceleration, highlighting the relationship between speed changes over time.

Sign Convention

Sign convention is the assignment of positive and negative values to directions in vector problems. It ensures consistency when calculating changes in velocity and acceleration, especially when the direction of motion reverses during an interval.

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