91Ó°ÊÓ

Velocity is a vector quantity, which means it has both magnitude and direction. It tells us how fast an object is moving and in which direction.
This is different from speed, which only considers how fast something is going, regardless of the direction.

• If an object is moving in a positive direction with a positive velocity, it’s speeding up in that direction.
• If it’s moving in a negative direction with a negative velocity, it’s also speeding up - but in the opposite way!
• When an object moves in the negative direction with a positive velocity, it is slowing down.

In our exercise, the particle starts moving with a velocity of \(4 \text{ m/s}\) in the positive X direction.
This means it starts by moving to the right at the speed of \(4 \text{ m/s}\).
However, since acceleration acts in the opposite direction, the velocity will change over time.

Acceleration is another vector quantity that tells us how the velocity of an object is changing over time. If you think of velocity as speed and direction, then acceleration is the rate at which speed and/or direction is changing.
Acceleration can be positive or negative:

• Positive acceleration means the object is speeding up in its current direction.
• Negative acceleration, often called deceleration, means the object is slowing down.

In the provided exercise, the particle has an acceleration of \(-1 \text{ m/s}^2\).
The negative sign shows that the acceleration opposes the direction of velocity.
This opposition causes the particle to slow down, as the velocity is reduced by \(1 \text{ m/s}\) every second it moves.
After 10 seconds, this negative acceleration completely reverses the particle's velocity from \(4 \text{ m/s}\) to \(-6 \text{ m/s}\).
Understanding how the acceleration affects velocity over time is key in predicting motion.

Equations of motion help describe an object's motion in terms of its velocity, acceleration, time, and displacement. These foundational equations allow us to calculate key aspects of motion, as in the provided exercise.
In this case, two equations are particularly useful:

• The first is the equation for final velocity: \[ v_f = v_i + a \times t \] Here, \( v_f \) is the final velocity, \( v_i \) is the initial velocity, \( a \) is the acceleration, and \( t \) is the time.
• The second is the equation for displacement or distance: \[ s = v_i \times t + \frac{1}{2} a t^2 \] This calculates displacement \( s \) by considering both the initial velocity and the effect of acceleration over time.

Applying these equations in our problem:
We first calculated the final velocity, finding it to be \(-6 \text{ m/s}\).
Then, by using the displacement formula, we find that the particle's total movement was \(10 \text{ m}\) over \(10\) seconds.
These equations bring clarity and precision in understanding complex motion.