When a bus is accelerating, it must be

1. Analyze the question

The question asks for the definition of acceleration in the context of a moving bus. We need to distinguish between speed, velocity, and position to identify what must happen for acceleration to occur.

2. Explain the concept

In physics, acceleration is defined as the rate of change of velocity with respect to time.

It is crucial to understand the difference between speed and velocity:

• Speed is a scalar quantity (it only has magnitude).
• Velocity is a vector quantity (it has both magnitude and direction).

Because velocity includes direction, an object is accelerating if:

1. Its speed changes (speeding up or slowing down).
2. Its direction changes (even if the speed remains constant, like a car turning a corner).
3. Both its speed and direction change.

3. Show the solution

• Option A (changing its speed): While changing speed is a form of acceleration, it is not the only way to accelerate. An object moving at a constant speed in a circle is still accelerating because its direction is changing.
• Option B (changing its velocity): Since velocity is defined as "speed in a given direction," any change in either speed or direction results in a change in velocity. Therefore, acceleration is defined as a change in velocity.
• Option C (changing its position): An object can change its position (move) at a constant velocity (zero acceleration). Therefore, this is not the definition of acceleration.
• Option D (changing its direction): Similar to Option A, this is only one specific type of acceleration.

Since acceleration is mathematically defined as $a = \frac{\Delta v}{\Delta t}$ (where $v$ is velocity), the bus must be changing its velocity.

4. Identify the answer

The correct option is B.

5. Tip

Think of the "Velocity Vector": If you are driving a bus and you either press the gas pedal (change speed) or turn the steering wheel (change direction), you are changing your velocity. Both actions count as acceleration!