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In physics, constant acceleration means that the rate of change of velocity remains uniform over time. This simplifies calculations since the acceleration value does not vary during the motion. Acceleration is denoted by \( a \), and it is usually measured in meters per second squared (\( \mathrm{m/s^2} \)). In the exercise, the car's acceleration is described as constant. This helps us calculate the change in speed and the distance traveled.
In many motion problems, constant acceleration allows the use of specific kinematic equations. These equations make it straightforward to compute unknown variables such as distance or time.
When dealing with motion, constant acceleration can arise in everyday situations such as a car speeding up or slowing down on a straight road. The key takeaway is that when acceleration is constant, calculations become more straightforward, allowing for the efficient use of formulas.

Equations of motion are fundamental tools in physics that connect the concepts of velocity, acceleration, time, and displacement. These equations are especially convenient when acceleration is constant, simplifying the study of object movement.
For the car in the exercise, we have two critical equations:

• Acceleration: \( a = \frac{v-u}{t} \)
• Distance: \( s = ut + \frac{1}{2}at^2 \)

Here, \( v \) is the final velocity, \( u \) is the initial velocity, \( a \) is acceleration, \( t \) is time, and \( s \) is displacement.
By substituting known values into these equations, one can easily find unknown variables, such as acceleration or distance, as demonstrated in the solutions. Learning to use these equations is crucial for solving problems involving linear motion under constant acceleration.
It's essential to identify which variable remains constant and which are changing to apply the right equation effectively.

Initial and final velocities are components of motion that describe an object's speed at different times. The initial velocity \( u \) refers to how fast an object is moving at the start of a time interval, while the final velocity \( v \) represents its speed at the end.
In the given exercise, the car starts with an initial velocity of \( 12 \, \mathrm{m/s} \) and reaches a final velocity of \( 21 \, \mathrm{m/s} \). The change from initial to final velocity indicates acceleration, showing how swiftly or gradually the car speeds up.
Knowing both velocities is crucial for computing acceleration using the formula \( a = \frac{v-u}{t} \). It also helps in determining other motion parameters like distance traveled. These factors are intertwined in equations of motion, underlining their importance in kinematic studies.