Understanding Acceleration in a 100-metre Sprint

Let's analyze what happens during the acceleration phase of a 100-metre sprint when an athlete is speeding up. We need to consider the concepts of velocity and acceleration and their directions.

Defining Velocity and Acceleration

• Velocity: This is a vector quantity that describes both the speed and the direction of motion. In a 100-metre sprint, the direction is typically straight forward.
• Acceleration: This is also a vector quantity. It is the rate at which velocity changes. If an object is speeding up, slowing down, or changing direction, it is accelerating.

Direction Convention

For a straight-line motion like a 100-metre sprint, we can define a positive direction. It is standard to define the direction of motion (forward) as the positive direction.

Analyzing the Acceleration Phase when Speeding Up

When the athlete is speeding up in the acceleration phase, their speed is increasing. Since the motion is forward, the velocity vector is in the positive direction. For the speed to increase, the acceleration must be in the same direction as the velocity.

• If velocity $\vec{v}$ is in the positive direction (forward), and the speed $|\vec{v}|$ is increasing, then the acceleration $\vec{a}$ must also be in the positive direction.
• Think of it this way: acceleration adds to the velocity. If you want to increase velocity in the positive direction, you must add a positive acceleration.

Evaluating the Options

Let's look at each option based on our understanding:

1. Direction of the acceleration is negative

   This would mean the acceleration is in the opposite direction of motion (backward). If the acceleration were negative while the velocity is positive, the athlete would be slowing down, not speeding up.

2. Direction of motion is negative

   In a standard 100-metre sprint, the athlete moves forward from the start line towards the finish line. We define this forward direction as positive. Therefore, the direction of motion is positive, not negative.

3. Direction of velocity is constant

   During a straight 100-metre sprint, the direction of velocity is indeed constant (forward, which we defined as positive). However, the question asks about the direction of *acceleration* when speeding up. While velocity direction is constant, the velocity *magnitude* (speed) is changing, which is caused by acceleration. This option describes velocity, but not what directly happens with acceleration's direction during speeding up.

4. Direction of the acceleration is positive

   As established, when an object is moving in the positive direction and speeding up, the acceleration must be in the same positive direction to increase the magnitude of the positive velocity.

Therefore, if you are speeding up in the acceleration phase of a 100-metre sprint (moving forward), the direction of the acceleration is positive.

Revision Table: Key Concepts in Sprint Acceleration

Additional Information: Velocity vs. Speed and Acceleration

It's important to distinguish between speed and velocity, and how acceleration affects them:

• Speed is the magnitude of velocity. It's a scalar (just a number, like 10 m/s).
• Velocity is speed plus direction (like 10 m/s East).
• Acceleration tells us how the velocity changes.
• If velocity and acceleration are in the same direction, the object speeds up.
• If velocity and acceleration are in opposite directions, the object slows down (this is also called deceleration, but it's just acceleration in the opposite direction of motion).
• If acceleration is perpendicular to velocity, the object changes direction but not necessarily speed (like in circular motion). This isn't relevant for a straight sprint.

In the initial acceleration phase of a sprint, the goal is to increase speed rapidly in the forward direction, hence the positive acceleration.