Velocity is a term used to describe the speed and direction of an object’s movement. An object that is at rest has a velocity of zero because it is not moving. This means there is no speed or direction associated with the object when it is at rest. Understanding what it means for an object to be at rest in terms of velocity is important in physics when analyzing motion and forces.
Defining Velocity
Velocity is defined as the rate at which an object’s position changes over time. It is calculated by dividing the displacement of an object by the time it took to cover that displacement. Velocity accounts for both the speed and direction of motion.
| Symbol | Definition |
|---|---|
| v | Velocity |
| Δs | Displacement |
| Δt | Change in time |
The equation for velocity is:
v = Δs/Δt
Where v is velocity, Δs is displacement, and Δt is change in time. Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. The units for velocity are typically meters/second (m/s) or feet/second (ft/s).
Speed vs. Velocity
Speed and velocity are related but distinct terms. Speed refers only to how fast an object is moving, while velocity accounts for both speed and direction. An object moving north at 50 mph, for example, has a speed of 50 mph and a velocity of 50 mph north.
At Rest Velocity
When an object is at rest, it means it is not moving and its position is constant. An object at rest has a velocity of zero because it has no displacement over time. With no change in position, the displacement Δs is zero. This makes the velocity:
v = 0/Δt = 0
So an object at rest has:
– A speed of 0 m/s or 0 ft/s
– No direction associated with its motionless state
– A velocity of 0 m/s or 0 ft/s
Some key points about velocity when an object is at rest:
– The object’s position does not change over time. Without a change in position, there is no displacement.
– With no displacement occurring, the velocity must be zero since the displacement Δs is zero in the velocity equation.
– Velocity is a vector, so a zero velocity means no speed and no direction.
– A zero velocity does not mean the object has no potential to move, just that it is not moving at that particular time. Force can still act on the motionless object.
– Contrast to objects moving at a constant velocity, which have non-zero velocities because their positions are continuously changing over time.
Examples of Objects at Rest
There are many examples of objects at rest in everyday life:
– A book sitting on a table has zero velocity.
– A car stopped at a red light is at rest, even though it has the potential to move when the light turns green.
– A ball before it is thrown has zero velocity. Once thrown it gains a non-zero velocity.
– A crate stationary on a flatbed truck is at rest, even as the truck moves underneath it.
– Any object that is stationary and not in motion, no matter how brief, is considered at rest and has zero velocity.
Describing Motion with Velocity-Time Graphs
Motion can be visually represented on velocity-time graphs. These graphs plot an object’s velocity over time. The velocity at any point can be read off the y-axis, while the x-axis shows the passage of time.
When an object is at rest, it is represented on a velocity-time graph as a horizontal line at zero velocity:
Key things the horizontal line indicates:
– Zero velocity means no motion.
– Constant position over time, since there is no change.
– Vertical rise of zero on the graph over any time interval.
– At rest state continues as long as line remains horizontal at v=0.
Comparing Motion and Rest
Contrasting horizontal lines for rest states with angled lines representing motion further clarifies the meaning of zero velocity:
– Angled lines indicate non-zero velocities and changing positions over time.
– Steeper angled lines represent faster motion (greater velocity change over time).
– Horizontal lines represent zero velocity at rest with no change in position.
At Rest and Newton’s First Law of Motion
Newton’s First Law of Motion helps explain the velocity of an object at rest:
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.
This law establishes that objects resist changes in their state of motion. So an object at rest remains at rest, with a velocity of zero, unless a net external force acts on it. And an object in motion continues moving at a constant velocity unless forced to change.
Examples:
– A ball on the grass remains at rest since no forces act on it. To set it in motion, a force like a kick must be applied.
– A car in motion continues moving at a constant velocity unless brakes or friction slow it down.
Newton’s First Law helps reinforce why at rest objects have zero velocity – they will not change position or move unless an unbalanced force causes them to accelerate to a non-zero velocity.
At Rest Velocity in Terms of Motion Graphs
Looking at velocity-time and position-time graphs helps visualize motion versus rest:
Velocity-Time Graphs
– Motion: Angled line showing changing velocity over time.
– Rest: Horizontal line at v=0 m/s.
Position-Time Graphs
– Motion: Angled line showing position changing over time.
– Rest: Horizontal line at constant position.
Key observations:
– Motion results in angled graphs showing change.
– Rest results in horizontal graphs showing no change.
– The slope of angled lines indicates velocity on velocity-time graphs.
– Zero velocity at rest means no change in position over time.
Examples of Calculating Velocity
Velocity calculations further demonstrate the meaning of zero velocity for objects at rest:
Example 1
A stationary ball has no movement.
– Displacement (Δs) = 0 m (no change in position)
– Time (Δt) = 5 s
– Velocity = Δs/Δt
= 0 m/5 s
= 0 m/s
The ball at rest has zero velocity.
Example 2
A car travels 50 m north over 10 s at constant velocity.
– Displacement (Δs) = 50 m
– Time (Δt) = 10 s
– Velocity = Δs/Δt
= 50 m/10 s
= 5 m/s north
The moving car has a non-zero constant velocity.
Significance of Zero Velocity in Physics Problems
Identifying when objects have zero velocity is important when solving physics problems involving motion and forces. Key ways velocity of zero matters:
– Determines if an object needs to be accelerated to a non-zero velocity. Objects at rest (v=0) must be accelerated by a net force before beginning motion.
– Allows separating motion into segments with constant non-zero velocities and segments at rest (v=0) in between, like an object oscillating on a spring.
– Simplifies calculations using kinematic equations. For intervals where v=0, motion equations reduce and simply show no change in position.
– Recognizing when velocity is zero identifies when forces are balanced and no acceleration occurs, according to Newton’s Second Law.
– Reveals intervals where work is not being done on an object, since no displacement is occurring.
– Indicates when kinetic energy is zero before or after motion takes place.
So carefully identifying situations where an object’s velocity is zero provides key insights into analyzing motion problems.
Practice Problems and Examples
Let’s work through some practice problems to apply the concepts of velocity for objects at rest:
Example 1
A soccer ball sits on the field before being passed between players. Determine its velocity.
– The ball is stationary and not moving, so its position is unchanging.
– With no displacement, Δs = 0 m.
– The velocity equation is v = Δs/Δt
– Plugging in Δs = 0 m gives v = 0 m/s
Therefore, the velocity of the ball at rest is 0 m/s.
Example 2
A hockey puck slides across the ice at 10 m/s north for 5 seconds. Then it rests on the ice for 3 seconds before being passed. What is its velocity during the 3 second rest period?
– While at rest, the puck’s position does not change for 3 seconds.
– With no change in position, the displacement Δs = 0 m.
– Using the velocity equation:
v = Δs/Δt
Δs = 0 m
Δt = 3 s
– The velocity during the 3 second rest is v = 0 m/3 s = 0 m/s
The velocity is zero while the puck is at rest on the ice.
Example 3
On a velocity-time graph, a horizontal line segment extends from t=10 s to t=15 s. What does this represent?
– A horizontal line at v=0 m/s on a velocity-time graph indicates zero velocity.
– Zero velocity means the object is at rest and not moving.
– Therefore, the horizontal segment from 10 s to 15 s shows the object is at rest during that time interval.
– Its position is constant over that segment since it has zero velocity.
Conclusion
In physics, an object that is at rest has a velocity of zero. This means it has no movement, so its position remains constant and no displacement occurs over time. With no displacement, the velocity equation v = Δs/Δt equates to zero for an object at rest.
Velocity encompasses both the speed and direction of motion. So zero velocity means no speed and no associated direction. On graphs, objects at rest are represented by horizontal lines on both velocity-time and position-time plots, indicating no change. Identifying when objects have zero velocity provides key insights when analyzing motions problems involving forces and energy. Carefully noting rest states versus intervals of non-zero constant velocities enhances the ability to model and calculate motion parameters accurately.