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Acceleration is a measure of how quickly an object's velocity changes over time. When the sprinter begins her race, her acceleration is positive, implying that she is speeding up. In the context of physics, acceleration is expressed in meters per second squared (m/s²). This unit indicates the increase in meters per second of the velocity for every second of acceleration.
In our exercise, the sprinter experiences an initial acceleration of 2.3 m/s². This means that for each second, her velocity increases by 2.3 m/s. Acceleration can be caused by forces such as the sprinter pushing off from the starting block. It's important to note that acceleration can be either positive or negative, where negative acceleration (deceleration) implies slowing down.

Velocity describes how fast an object is moving in a specific direction. Unlike speed, which is scalar and does not account for direction, velocity is a vector. It includes both the magnitude (speed) and the direction of motion.
Initially, our sprinter starts from rest, meaning her initial velocity is zero (0 m/s). As she accelerates, her velocity increases according to the equation: \[ v = v_0 + a \cdot t \]Where \( v_0 \) is the initial velocity, \( a \) is the acceleration, and \( t \) is the time. By substituting the given values, we find that her velocity at 1.2 seconds after the start equals 2.76 m/s. After this, she maintains this velocity for the remainder of the race, assuming no other forces are acting.

Constant velocity means maintaining a steady speed in a fixed direction. Once our sprinter's acceleration becomes zero, her velocity does not change. This is what we observe after the initial 1.2 seconds of acceleration.
In physics, when an object's acceleration is zero, its velocity is constant. So, the sprinter continues the race at a constant velocity of 2.76 m/s. This indicates no external forces are causing the sprinter to speed up or slow down after the initial burst. Understanding constant velocity is crucial for analyzing motion, especially in the context of uniform motion where the speed and direction remain unchanged.

The equations of motion provide formulas to describe the motion of an object under certain conditions. These equations relate velocity, acceleration, time, and displacement.
For the sprinter problem, we use the basic equation of motion for velocity: \[ v = v_0 + a \cdot t \]This equation is useful when you know the initial velocity, the acceleration, and the time duration of the acceleration. It helps calculate the final velocity after the period of acceleration. In this exercise, with an initial velocity of 0 m/s and acceleration of 2.3 m/s² sustained over 1.2 seconds, the sprinter's velocity becomes 2.76 m/s at the end of the acceleration phase.

• Always check units when using equations of motion, ensuring consistency.
• Understanding each variable's role helps facilitate problem-solving in kinematics.