Pointing the same way or the opposite way

The idea

Acceleration has magnitude and direction; in straight-line motion it is in the direction of velocity when the magnitude of velocity increases, and opposite to it, shown by a minus sign, when the magnitude decreases.

Accelerator and brake

A bus moves to the right along a straight highway. The driver first presses the accelerator and later presses the brake.

Do you think the acceleration points the same way in both cases?

• No, it points one way when speeding up and the other way when braking
• Yes, it points to the right in both cases
• Acceleration has no direction

Accelerator and brake

Press each button and compare the red arrow with the blue arrow.

Compare the arrows

When the bus speeded up, the red arrow pointed the same way as the blue one. When it braked, the red arrow pointed the other way, and the number was negative: −3 m s⁻².

Acceleration has magnitude and direction. In straight-line motion it is in the direction of the velocity when the magnitude of velocity increases, and opposite to the velocity when the magnitude decreases, shown by a minus sign.

Notes

If the magnitude of velocity increases, acceleration is along the velocity. If it decreases, acceleration is opposite, with a minus sign.

Check yourself

A bus moves to the right and its speed is increasing. The acceleration points…

A bus moves to the right and the driver presses the brake. The acceleration points…

What does a minus sign in the acceleration of a bus moving in the positive direction show?

The velocity of a bus falls from 15 m s⁻¹ to 0. Is the acceleration positive or negative (take the velocity as positive)?

• to the left, opposite to the velocity. The acceleration is opposite to the velocity only when the magnitude of the velocity decreases.
• to the right, in the direction of the velocity — correct. Yes!
• There is no acceleration. The velocity changes, so there is an acceleration.
• to the right, in the direction of the velocity. The acceleration is in the direction of the velocity only when the magnitude of the velocity increases.
• downwards. Along a straight highway the acceleration lies along the line of the motion, either with or against the velocity.
• to the left, opposite to the velocity — correct. Yes!
• The acceleration is opposite to the velocity because the magnitude of velocity is decreasing — correct. Yes!
• The bus is moving backwards. The minus sign shows the direction of the acceleration, not that the bus moves backwards.
• The bus is at rest. A bus at rest has zero velocity. The minus sign shows the acceleration is opposite to the velocity.
• Positive. The velocity is decreasing, so the acceleration is opposite to the velocity, which is a negative value.
• Negative — correct. Yes!
• Zero. The velocity changes, so the acceleration is not zero.