Let's break down this problem about an object moving with constant acceleration. We are given the starting condition, the acceleration, and the time elapsed, and we need to find the final speed.

Understanding the Problem of Constant Acceleration

The question describes a common scenario in kinematics, which is the study of motion. When an object moves with constant acceleration, its velocity changes at a steady rate. We can use specific equations, known as the equations of motion under constant acceleration, to relate initial velocity, final velocity, acceleration, time, and displacement.

Given Information for Calculating Speed

From the problem statement, we have the following information:

• The object starts from rest. This means its initial velocity (\(u\)) is 0 m/s.
• The object moves with a constant acceleration (\(a\)) of \(4 \text{ m/s}^2\).
• The time elapsed (\(t\)) is 8 s.

We need to find the final speed or final velocity (\(v\)) after 8 seconds.

Applying the Equation of Motion to Find Speed

We can use the first equation of motion, which directly relates initial velocity (\(u\)), final velocity (\(v\)), acceleration (\(a\)), and time (\(t\)):

\(v = u + at\)

Step-by-Step Calculation of Final Velocity

Now, let's substitute the given values into the equation:

Initial velocity, \(u = 0 \text{ m/s}\)

Acceleration, \(a = 4 \text{ m/s}^2\)

Time, \(t = 8 \text{ s}\)

The equation becomes:

\(v = (0 \text{ m/s}) + (4 \text{ m/s}^2) \times (8 \text{ s})\)

First, multiply the acceleration by the time:

\(v = 0 \text{ m/s} + (4 \times 8) \text{ m/s}\)

\(v = 0 \text{ m/s} + 32 \text{ m/s}\)

Now, add the initial velocity (which is zero in this case):

\(v = 32 \text{ m/s}\)

So, the final speed of the object after 8 seconds is 32 m/s.

Summarizing the Calculation

Here is a summary of the values and the result:

The calculation confirms that the speed after 8 seconds is 32 m/s.

Revision Table: Key Concepts in Constant Acceleration

Additional Information: Equations of Motion

For motion with constant acceleration, there are three main equations relating displacement (\(s\)), initial velocity (\(u\)), final velocity (\(v\)), acceleration (\(a\)), and time (\(t\)). These are often called the kinematic equations:

• Equation 1: \(v = u + at\) (Relates v, u, a, t)
• Equation 2: \(s = ut + \frac{1}{2}at^2\) (Relates s, u, a, t)
• Equation 3: \(v^2 = u^2 + 2as\) (Relates v, u, a, s)

In this problem, since we were given \(u\), \(a\), and \(t\) and asked for \(v\), the first equation \(v = u + at\) was the most direct one to use. Understanding which equation to use based on the given and unknown variables is crucial for solving kinematics problems involving constant acceleration.