91Ó°ÊÓ

Constant acceleration occurs when an object's velocity changes at a steady rate over time. This means that, for each second that passes, the change in velocity is the same. Unlike variable acceleration, where the rate of velocity change differs at various moments, constant acceleration allows for simpler calculations using straightforward formulas.
In our train problem, the train accelerates uniformly from rest, indicating that its acceleration is constant. This is depicted in the calculation of the acceleration, which remains at 0.94 m/s² during the given time interval.
An acceleration system like this is linear, meaning that if we plot the velocity over time on a graph, the line would be straight. This linearity greatly simplifies predictions regarding velocity at future points.

Calculating velocity when acceleration is constant involves using the foundational physics formula: \[ v = u + at \] where:

• \( v \) is the final velocity,
• \( u \) is the initial velocity,
• \( a \) is the acceleration,
• \( t \) is the time elapsed.

In our exercise, during the first 5.0 seconds, the train starts from rest, so its initial velocity \( u \) is 0. After calculating the acceleration as 0.94 m/s², the initial velocity is updated to 4.7 m/s.
For the additional 6.0 second period, this 4.7 m/s becomes the new initial velocity. Using the equation, we compute the final velocity after the additional time to find the total change in speed to be 10.34 m/s.

Equations of motion are mathematical tools that describe the behavior of objects in motion. They relate displacement, velocity, acceleration, and time. Typically, for constant acceleration, there are three primary equations:

• \( v = u + at \) - to find final velocity.
• \( s = ut + \frac{1}{2}at^2 \) - to calculate displacement.
• \( v^2 = u^2 + 2as \) - to connect velocity and displacement without time.

For the train scenario, we utilized the first equation to predict the train's future speed after a known time period had passed.
This family of equations is highly versatile. They allow us to switch between finding speed, the distance covered, or how quickly an object is speeding up. Understanding when to apply each equation is made easier with practice and familiarity.