91Ó°ÊÓ

Equations of motion are essential tools in physics that describe how objects move under the influence of forces. These equations allow us to calculate an object's velocity, acceleration, and displacement over time. A common equation of motion is:

• \( v = u + at \)

where \( v \) is the final velocity, \( u \) is the initial velocity, \( a \) is acceleration, and \( t \) is time. This relationship tells us how an object's velocity changes over time when subjected to acceleration.
To determine acceleration, we must recall Newton's second law of motion:

• \( F = ma \),

where \( F \) is the force applied, \( m \) is the mass, and \( a \) is acceleration. By rearranging this equation, we find \( a = F/m \).
In our original exercise, a force \( F \) acts for 1 second on a body with a mass of 1 kg. Using the equations, we find that the final velocity is \( v_0 + F \), indicating that the force directly increases the velocity by \( F \).
These equations help us predict how fast an object will move if we know the force applied and the time it acts.

Momentum is a measure of an object's motion and is given by the product of its mass and velocity:

• \( p = mv \).

In physics, change in momentum is a critical concept because it reveals how forces affect motion. Often linked with impulse, the change in momentum tells us how an object's speed or direction alters.
In our exercise, the body starts with an initial momentum of \( mv_0 \). After 1 second, because of the force acting on it, the new velocity becomes \( v_0 + F \), making the final momentum \( m(v_0 + F) \).
The increase in momentum is calculated as:

• \( \Delta p = m(v_0 + F) - mv_0 = F \).

Here, as the mass is 1 kg, it simplifies to just the force \( F \). This illustrates how directly applying a force changes an object's momentum, which is fundamental to understanding motion in real-world applications.

Determining the distance an object travels under the influence of a force involves integrating its motion over time. One of the key equations for this purpose is the formula:

• \( s = ut + \frac{1}{2}at^2 \).

This tells us that the total distance \( s \) depends on its initial velocity \( u \), the acceleration \( a \), and the time \( t \) the force acts.
Applying this to our problem, the body's initial velocity is \( v_0 \) and acceleration is \( F \) (since mass is 1 kg). Think of \( s \) as the path the object traces as the force is exerted for 1 second.
So, substituting in, we find:

• \( s = v_0 \times 1 + \frac{1}{2}F \times 1^2 = v_0 + \frac{F}{2} \).

This equation reveals how both the initial speed and the force influence the distance traveled over a certain duration. Understanding this helps us quantify movement better, especially in scenarios where speed and external forces change concurrently.