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Uniform acceleration refers to a constant rate of change in velocity over time. In simpler terms, if an object is accelerating uniformly, its speed is increasing by the same amount every second. This makes calculations straightforward because once you know the initial speed and the acceleration, you can predict the object's future speed and position.

In the antelope problem, the animal is moving under uniform acceleration between two points. This means that its acceleration does not change as it travels the 70 meters. Knowing this helps us use kinematic equations to calculate other variables such as its initial speed. Uniform acceleration is a common assumption in physics problems that allows us to use some handy equations for further analysis.

Kinematic equations are tools physicists and engineers use to analyze the motion of objects under uniform acceleration. These equations help find unknown variables when others are known, such as distance, time, initial speed, final speed, and acceleration. For the given problem, we use two primary kinematic equations.

• The first equation, \( s = ut + \frac{1}{2} a t^2 \), is used to relate initial velocity \( u \), time \( t \), distance \( s \), and acceleration \( a \). This equation helps us determine how far an object travels under constant acceleration.
• The second key equation, \( v = u + at \), connects final speed \( v \), initial speed \( u \), acceleration \( a \), and time \( t \). It tells us how the velocity changes over time.

These equations are crucial in connecting different aspects of the motion in the problem. By substituting known values into these equations, we can methodically solve for the unknowns, as demonstrated in the solution steps.

Initial velocity is the speed of an object before it begins to accelerate. It's an essential starting point in many physics problems, such as the antelope's motion. When acceleration is uniform, we can calculate or deduce the initial velocity using kinematic equations.

In the antelope's case, we solved for its initial velocity using the data provided. We knew the final speed at the second point was 15 m/s, the time taken was 7 seconds, and the distance covered was 70 meters. With these details, we used the kinematic equation formulas to rearrange and simplify, eventually calculating that the initial velocity was 5 m/s.

Understanding initial velocity is important in predicting how an object will move, providing a foundation for further analysis involving speeds and distances in kinematic studies.