Calculating Final Velocity with Constant Acceleration

The question asks us to find the velocity of an object after a specific time, given its initial state (at rest) and its constant acceleration.

We are provided with the following information:

• Initial velocity (\(u\)) = 0 m/s (since the object starts from rest)
• Acceleration (\(a\)) = 5 m/s²
• Time (\(t\)) = 5 s

We need to find the final velocity (\(v\)) of the object after 5 seconds.

To solve this problem, we can use the first equation of motion (kinematic equation), which relates initial velocity, final velocity, acceleration, and time for objects moving with constant acceleration:

\(v = u + at\)

Where:

• \(v\) is the final velocity
• \(u\) is the initial velocity
• \(a\) is the acceleration
• \(t\) is the time taken

Now, we substitute the given values into the equation:

\(v = 0 \text{ m/s} + (5 \text{ m/s}^2)(5 \text{ s})\)

Performing the multiplication:

\(v = 0 \text{ m/s} + 25 \text{ m/s}\)

Calculating the final velocity:

\(v = 25 \text{ m/s}\)

Thus, the velocity of the object after 5 seconds is 25 m/s.

Let's compare this result with the given options:

The calculated velocity of 25 m/s matches Option 4.

Revision Table: Kinematic Equations Summary

Here are the primary kinematic equations used for motion with constant acceleration:

In these equations:

• \(s\) is the displacement
• \(u\) is the initial velocity
• \(v\) is the final velocity
• \(a\) is the acceleration
• \(t\) is the time

Additional Information: Understanding Acceleration

Acceleration is defined as the rate of change of velocity of an object. It is a vector quantity, meaning it has both magnitude and direction. The unit of acceleration is meters per second squared (\(m/s^2\)) in the SI system.

• When an object's velocity is increasing, its acceleration is in the same direction as its velocity. This is often called positive acceleration or simply acceleration.
• When an object's velocity is decreasing (slowing down), its acceleration is in the opposite direction to its velocity. This is often called negative acceleration or deceleration/retardation.
• If an object has zero acceleration, its velocity remains constant. If the object is moving, it continues to move at a constant speed in a straight line. If it is at rest, it remains at rest.

In this problem, the object has a constant positive acceleration of 5 m/s², meaning its velocity increases by 5 m/s every second in the direction of motion.