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Acceleration is a measure of how quickly an object speeds up or slows down. It is a vector quantity, which means it has both magnitude and direction. For an object that starts from rest and accelerates constantly, as in the case of Car A in the exercise, its acceleration is given by the rate of change of velocity over time.
The formula to calculate acceleration is:

• \( a = \frac{\Delta v}{t} \)

where \( a \) is the acceleration, \( \Delta v \) is the change in velocity, and \( t \) is the time over which the change occurs.
In the exercise, Car A has an acceleration of \(6.0 \mathrm{~m/s^2}\), which means each second it gains \(6.0 \mathrm{~m/s}\) in speed as long as it accelerates. Understanding acceleration helps predict how the speed of an object will increase over time.

Constant speed means that an object travels the same distance every second. This is the condition for Car B in the exercise. Unlike acceleration, constant speed implies no change in speed over time.
The formula to determine the distance covered at a constant speed is:

• \( s = v \times t \)

where \( s \) is the distance traveled, \( v \) is the constant speed, and \( t \) is the time of travel.
For Car B, moving at \(70.0 \mathrm{~m/s}\), it covers \(70.0\) meters every second. This steady pace is a great counterpoint to Car A's increasing speed, offering a clear view of how different speed conditions interact in motion.

Equations of motion are mathematical formulas used to describe the motion of an object under certain conditions. They can solve problems involving initial velocity, final velocity, acceleration, time, and displacement. They are essential tools in kinematics—the study of motion.
For uniformly accelerated motion, the main equations are:

• \( v = u + at \)
• \( s = ut + \frac{1}{2} at^2 \)
• \( v^2 = u^2 + 2as \)

where \( u \) is the initial velocity, \( v \) is the final velocity, \( a \) is the acceleration, \( s \) is the displacement, and \( t \) is the time.
In the given problem, we use the second equation to determine the distance Car A covers as it accelerates – starting from rest with a given acceleration over a defined time.

Relative motion is a concept used to describe the motion of an object as observed from another object. It's crucial in understanding how different frames of reference affect motion.
In the exercise, the motion of Car A is examined relative to Car B. The goal is for Car A to reach the same point as Car B and match its speed, even though they started with different initial conditions.
To solve such problems, it's helpful to consider:

• The position or distance each object has traveled since they started moving.
• The time it takes for the relative positions to equal each other.
• The speeds or accelerations, showing how an object increases or maintains its velocity compared to another object's movement.

Relative motion calculations often simplify complex problems by focusing on the differences in velocity, position, and time between objects. By understanding these concepts, predicting when and where two moving objects will intersect becomes straightforward.