The motion of a particle is described by the equation u = at. The distance travelled by the particle in the first 4 second.? Plzz explain hw to do this?

To find the distance traveled by a particle whose motion is described by the equation \( u = at \), we need to understand what this equation represents. Here, \( u \) is the velocity of the particle at time \( t \), and \( a \) is the constant acceleration. The equation indicates that the velocity increases linearly over time due to the constant acceleration. To determine the distance traveled in the first 4 seconds, we can use the relationship between distance, velocity, and time.

Understanding the Relationship Between Distance and Velocity

The distance traveled by an object under constant acceleration can be calculated using the formula:

• d = ut + (1/2)at²

In this formula:

• d is the distance traveled.
• u is the initial velocity (which is zero if the particle starts from rest).
• a is the constant acceleration.
• t is the time duration.

Step-by-Step Calculation

Let’s break down the calculation step by step. Assuming the particle starts from rest, the initial velocity \( u \) at \( t = 0 \) is 0. Therefore, we can simplify our distance formula:

• Since \( u = 0 \), the formula becomes: d = (1/2)at²

Now, we need to plug in the values. We know the time \( t \) is 4 seconds. However, we also need the value of acceleration \( a \). If you have a specific value for \( a \), you can substitute it in. For example, let’s say \( a = 2 \, \text{m/s}² \) (you can replace this with any value you have).

Calculating Distance

Substituting the values into the formula:

• d = (1/2) * 2 * (4)²
• d = (1/2) * 2 * 16
• d = 1 * 16
• d = 16 \, \text{meters}

So, if the acceleration is \( 2 \, \text{m/s}² \), the particle would travel 16 meters in the first 4 seconds. If you have a different value for acceleration, just substitute that into the formula and follow the same steps to find the distance.

Summary of the Process

To summarize, the key steps are:

• Identify the initial velocity and acceleration.
• Use the distance formula for uniformly accelerated motion.
• Substitute the known values into the formula.
• Calculate the distance.

By following these steps, you can easily determine the distance traveled by a particle under constant acceleration for any given time period. If you have any specific values or further questions, feel free to ask!