Question

determine the cause of acceleration in each scenario.
an airplane turning from south to west at constant speed is accelerating due to a change in
a biker going 7 m/s west after travelling north at 5 m/s is accelerating due to a change in
a runaway shopping cart speeding up as it goes down a hill is accelerating due to a change in

Explanation:

To solve this, we recall that acceleration is caused by a change in velocity, and velocity is a vector with magnitude (speed) and direction. So we analyze each scenario:

Scenario 1: Airplane turning (constant speed)

Acceleration occurs here because the direction of the airplane’s velocity is changing (from south to west), even though speed is constant.

Scenario 2: Biker changing direction (and speed)

The biker was moving north (direction) at 5 m/s (speed) and then moves west (new direction) at 7 m/s (new speed). So both speed and direction (components of velocity) change, causing acceleration.

Scenario 3: Shopping cart speeding up (change in speed)

The cart’s speed is increasing as it goes down the hill (magnitude of velocity is changing), so acceleration is due to a change in speed.

Final Answers (filling the blanks):

1. An airplane turning from south to west at constant speed is accelerating due to a change in $\boldsymbol{\text{direction}}$.
2. A biker going 7 m/s west after travelling north at 5 m/s is accelerating due to a change in $\boldsymbol{\text{speed and direction}}$ (or "velocity components," but "speed and direction" is clearer here).
3. A runaway shopping cart speeding up as it goes down a hill is accelerating due to a change in $\boldsymbol{\text{speed}}$.

(Note: For the second scenario, "velocity" could also be a valid answer, but breaking it into "speed and direction" is more precise since both are changing.)

Answer:

To solve this, we recall that acceleration is caused by a change in velocity, and velocity is a vector with magnitude (speed) and direction. So we analyze each scenario:

Scenario 1: Airplane turning (constant speed)

Acceleration occurs here because the direction of the airplane’s velocity is changing (from south to west), even though speed is constant.

Scenario 2: Biker changing direction (and speed)

The biker was moving north (direction) at 5 m/s (speed) and then moves west (new direction) at 7 m/s (new speed). So both speed and direction (components of velocity) change, causing acceleration.

Scenario 3: Shopping cart speeding up (change in speed)

The cart’s speed is increasing as it goes down the hill (magnitude of velocity is changing), so acceleration is due to a change in speed.

Final Answers (filling the blanks):

1. An airplane turning from south to west at constant speed is accelerating due to a change in $\boldsymbol{\text{direction}}$.
2. A biker going 7 m/s west after travelling north at 5 m/s is accelerating due to a change in $\boldsymbol{\text{speed and direction}}$ (or "velocity components," but "speed and direction" is clearer here).
3. A runaway shopping cart speeding up as it goes down a hill is accelerating due to a change in $\boldsymbol{\text{speed}}$.

(Note: For the second scenario, "velocity" could also be a valid answer, but breaking it into "speed and direction" is more precise since both are changing.)