Question

which of the following statements are true? choose all that apply. hint: the statements that are

an object can simultaneously speed up and have negative acceleration.

an object can simultaneously have positive velocity and have a constant position.

an object can simultaneously have constant position and have zero velocity.

an object can simultaneously have negative speed and have constant velocity.

an object can simultaneously be traveling a negative distance and have non - zero velocity.

an object can simultaneously slow down and have zero acceleration.

Explanation:

Step1: Analyze the first statement

Acceleration is the rate of change of velocity. If an object is moving in the negative direction and its speed is increasing (e.g., - 2 m/s to - 4 m/s), it has negative acceleration and is speeding up. So, an object can simultaneously speed up and have negative acceleration.

Step2: Analyze the second statement

If an object has a positive velocity, its position is changing. Velocity \(v=\frac{\Delta x}{\Delta t}\), if \(v>0\), \(\Delta x>0\) (assuming \(\Delta t>0\)). So, an object cannot simultaneously have positive velocity and a constant position.

Step3: Analyze the third statement

If an object has a constant position (\(\Delta x = 0\)), then its velocity \(v=\frac{\Delta x}{\Delta t}=0\). So, an object can simultaneously have a constant position and zero velocity.

Step4: Analyze the fourth statement

Speed is a non - negative quantity (\(v=\vert\vec{v}\vert\geq0\)). So, an object cannot have a negative speed.

Step5: Analyze the fifth statement

Distance is a non - negative quantity (\(d\geq0\)). So, an object cannot travel a negative distance.

Step6: Analyze the sixth statement

Acceleration \(a=\frac{\Delta v}{\Delta t}\). If an object is slowing down, \(\Delta v
eq0\) (either \(v_{f}0\) or \(v_{f}>v_{i}\) when \(v < 0\)). So, \(a
eq0\) when an object is slowing down.

Answer:

An object can simultaneously speed up and have negative acceleration. An object can simultaneously have constant position and have zero velocity.