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A retarding force is a type of force that slows down an object in motion. It acts in the opposite direction to the movement of the object. In simple terms, if an object is moving one way, a retarding force pulls it back the other way. This type of force is crucial when we need to bring an object to a halt or reduce its speed.

In the exercise example, a retarding force of 50 N is applied to a moving body. Since this force is constant, it affects the body in a steady, uniform way, continuously reducing the object's speed over time. Understanding how a retarding force operates involves Newton's laws of motion.

• Newton's first law tells us that a body will remain in motion unless acted upon by an external force—like a retarding force.
• Newton's second law helps us calculate the effect of this force by using the formula: \( F = m \times a \).

In any scenario with a retarding force, knowing the magnitude of this force and how it applies to the object in question is vital to calculating other motion-related variables such as acceleration and stopping time.

Acceleration is the rate at which the velocity of an object changes over time. When we want to find how fast an object is slowing down or speeding up, we calculate its acceleration. Using Newton's second law, we can determine acceleration using the formula \( a = \frac{F}{m} \).

For the body in the exercise, we were given a retarding force of 50 N and a mass of 20 kg. Plugging these into the formula gives: \[ a = \frac{50 \, \text{N}}{20 \, \text{kg}} = 2.5 \, \text{m/s}^2 \]
Since the force acts against the direction of motion, this acceleration is negative: \( a = -2.5 \, \text{m/s}^2 \).

This negative sign indicates that the object is decelerating or slowing down.

• Remember, a positive acceleration means an increase in speed.
• A negative acceleration, or deceleration, suggests a decrease in speed, hence why it's used here to stop the body.

Calculating the acceleration correctly sets the foundation for determining other aspects of motion, such as the time it takes for the object to stop.

Equations of motion are a set of formulas used to solve problems involving the motion of an object under uniform acceleration. They describe the relationship between displacement, velocity, time, and acceleration. In the given exercise, we particularly focus on the equation that relates initial velocity, final velocity, acceleration, and time:

\[ v = u + at \]
Where:

• \( v \) is the final velocity (0 m/s here, as the body stops).
• \( u \) is the initial velocity (15 m/s in this situation).
• \( a \) is the acceleration (-2.5 m/s²).
• \( t \) is the time to come to a stop.

To find the time, we rearrange the equation: \[ t = \frac{v - u}{a} \]
Substituting the given values provides us with: \[ t = \frac{0 - 15}{-2.5} = 6 \, \text{seconds} \]
Equations of motion allow us to predict how long it will take for objects to reach a certain speed or position. By applying these equations, you can analyze various practical scenarios in physics, making them invaluable tools in solving real-world problems.