Question

the acceleration due to gravity on earth is _____.
-9.81 m
-9.81 m/s
-9.81 m/s^2
-9.81 s

based on the velocity vs. time graph below, the object is ______ between 30 and 40 seconds.
graph 1: velocity vs time
v (m/s)
20
10
10 20 30 40 time (s)
at rest
not moving
slowing down
speeding up

which object has the least amount of inertia?
5 kg book

Explanation:

First Question (Acceleration due to Gravity)

Step1: Recall unit of acceleration

Acceleration is the rate of change of velocity, so its unit is length per time squared.

Step2: Analyze options

• \(-9.81\ \text{m}\): Unit of length, not acceleration.
• \(-9.81\ \text{m/s}\): Unit of velocity, not acceleration.
• \(-9.81\ \text{m/s}^2\): Unit of acceleration (length/time²), correct for gravitational acceleration.
• \(-9.81\ \text{s}\): Unit of time, incorrect.

Step1: Interpret velocity - time graph

In a velocity - time graph, the slope represents acceleration. If velocity is decreasing (slope negative) while moving, the object is slowing down. Between 30 and 40 seconds, the velocity decreases from a positive value to 0.

Step2: Analyze options

• "at rest": Velocity would be 0, but here velocity is decreasing from non - zero to 0, not at rest initially.
• "not moving": Velocity is changing, so it is moving (decelerating).
• "slowing down": Since velocity is decreasing (from, say, 15 m/s to 0 between 30 - 40 s), the object is slowing down.
• "speeding up": Velocity is decreasing, not increasing.

Step1: Recall inertia - mass relation

Inertia is directly proportional to mass (\(I\propto m\)). Lower mass means lower inertia.

Step2: Compare masses

A 5 kg book has less mass than a 10 kg object (assuming the second option is 10 kg). So the 5 kg book has the least inertia.

Answer:

\(-9.81\ \text{m/s}^2\) (the option with \(-9.81\ \text{m/s}^2\))

Second Question (Velocity vs Time Graph)