Question

1. what is the total displacement of the object?
2. use the velocity - time graph below to answer the following questions.
3. what is the objects velocity at t = 10s?
4. what is the objects acceleration from t = 2s to t = 5s?
5. during which time intervals is the object traveling at a constant speed?
6. during which time intervals is the object moving to the left (negative velocity)?
7. what is the objects acceleration from t = 11s to t = 18s?
8. state newtons first law of motion.
9. what one word can be used to describe newtons first law?
10. what two things could an object be doing if the net force acting on it is 0?
11. if a 0.17 kg hockey puck was sliding on frictionless ice, how much force would be needed to keep it moving at a constant velocity of 7 m/s?
12. what property of matter determines how much inertia an object has?
13. why do we generally not see objects in motion continue to move at a constant velocity?
14. compare and contrast mass and weight.
15. what is the formula for calculating an objects weight?
16. a 30 kg object sits at rest on a table.

a. draw a free - body diagram for the forces acting on the object.

Explanation:

Step1: Identify the velocity - time graph problem

We are given a velocity - time graph and need to answer questions related to velocity, acceleration, and motion characteristics.

Step2: Answer part a

To find the velocity at \(t = 10s\), we look at the value of the velocity - time graph at \(t=10s\). From the graph, the velocity \(v(10)=2m/s\).

Step3: Answer part b

Acceleration \(a=\frac{\Delta v}{\Delta t}\). From \(t = 2s\) to \(t = 5s\), \(v(2)=0m/s\) and \(v(5)= - 4m/s\). So \(a=\frac{v(5)-v(2)}{5 - 2}=\frac{-4 - 0}{3}=-\frac{4}{3}m/s^{2}\).

Step4: Answer part c

The object travels at a constant speed when the magnitude of velocity does not change. From the graph, this occurs in the intervals \(5 - 10s\) and \(15 - 20s\).

Step5: Answer part d

The object moves to the left (negative velocity) in the intervals \(2 - 5s\) and \(10 - 15s\).

Step6: Answer part e

From \(t = 15s\) to \(t = 18s\), \(v(15)=-6m/s\) and \(v(18)=0m/s\). Acceleration \(a=\frac{v(18)-v(15)}{18 - 15}=\frac{0+6}{3}=2m/s^{2}\).

Step7: Answer part 8

Newton's first law of motion states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Step8: Answer part 9

The word 'inertia' can be used to describe Newton's first law.

Step9: Answer part 10

If the net force acting on an object is 0, the object could be at rest or moving at a constant velocity.

Step10: Answer part 11

According to Newton's first law, if there is no net force (\(F_{net}=0\)), an object will move at a constant velocity. So, for a \(0.17kg\) hockey - puck sliding on frictionless ice, the force needed to keep it moving at a constant velocity of \(7m/s\) is \(F = 0N\).

Step11: Answer part 12

The mass of an object determines how much inertia it has.

Step12: Answer part 13

We generally do not see objects in motion continue to move at a constant velocity because there are usually non - zero net forces acting on them, such as friction, air resistance, etc.

Step13: Answer part 14

Mass is a measure of the amount of matter in an object and is a scalar quantity. Weight is the force exerted on an object due to gravity (\(W = mg\)) and is a vector quantity. Mass is constant everywhere in the universe, while weight depends on the gravitational acceleration of the location.

Step14: Answer part 15

The formula for calculating an object's weight is \(W=mg\), where \(m\) is the mass of the object and \(g\) is the acceleration due to gravity (\(g\approx9.8m/s^{2}\) on Earth).

Step15: Answer part 16a

For a \(30kg\) object at rest on a table, the forces acting on it are the gravitational force \(F_g=mg\) (downward) and the normal force \(N\) (upward). The free - body diagram would have a downward arrow labeled \(F_g = 30\times9.8 = 294N\) and an upward arrow labeled \(N = 294N\) (since the object is at rest, \(F_{net}=0\) and \(N=F_g\)).

Answer:

a. \(2m/s\)
b. \(-\frac{4}{3}m/s^{2}\)
c. \(5 - 10s\) and \(15 - 20s\)
d. \(2 - 5s\) and \(10 - 15s\)
e. \(2m/s^{2}\)

1. An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
2. Inertia
3. At rest or moving at a constant velocity
4. \(0N\)
5. Mass
6. There are usually non - zero net forces (such as friction, air resistance) acting on them.
7. Mass is a measure of the amount of matter (scalar), weight is the force due to gravity (\(W = mg\), vector). Mass is constant, weight depends on \(g\).
8. \(W = mg\)

16a. Free - body diagram with downward arrow \(F_g=294N\) and upward arrow \(N = 294N\)