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Can a car reach terminal velocity?

Can a car reach terminal velocity?

1st Law : An object will remain at rest or in a uniform motion in a straight line unless acted upon by an unbalanced force.
From 1st Law, we have the idea of inertia which is the resistance of an object to a change in its state of motion or rest.

2nd Law : The resultant force on an object is proportional to the product of its mass and acceleration.
From 2nd Law, we have the formula F = ma , F is resultant force, m is mass, a is acceleration.

3rd Law : For every action, there is an equal and opposite reaction.

Worked problems on Newton’s Second Law (F = ma) (Part 1)

In this video, the first problem is a simple and common one. The second problem is more complicated which may not be asked during O levels. This complicated type of problem is more relevant to students from integrated program schools. However, it is also good that O level students go through this complicated problem to train your mind to think more indepth as there is application of forming of equations which is relevant to mathematics to solve this problem. Afterall, all these problems are just depending on the physics formula F = ma to solve them.

Worked problems on Newton’s Second Law (F = ma) (Part 2)

This video is a continuation to the part 1 video above. The complicated problem from the earlier part 1 video can be solved by another simpler way which does not involve forming of equations (see this video).

The next problem in this video is a terminal velocity problem. Take note that when an object is falling at constant terminal velocity, its acceleration MUST BE 0 ms-² since it is no longer accelerating at constant terminal velocity. At this instant, the object’s force of weight acting downwards MUST BE EQUAL to the force of air resistance acting upwards. The object’s resultant force will therefore be 0 N as well. The working is as follows.

Resultant force of person falling = Force of weight — Force of air resistance ,

Since Force of weight and Force of air resistance ARE EQUAL at terminal velocity, these two forces subtract to give resultant force to be 0 N.

As F = ma , assuming the person’s mass is 60 Kg, when resultant force F = 0 N at terminal velocity,
0 = 60 X a
a = 0 ms-²
Thus, a which is acceleration must be 0 ms-² at terminal velocity. Recall that terminal velocity is a constant velocity reached while falling. So, there must not be any acceleration if the person is now moving at constant terminal velocity.

We arrive at the conclusion for this kind of falling problem involving terminal velocity, there are two important concepts which can be simply understood.
First concept: Resultant force on object falling at terminal velocity is 0 N.
Second concept: Acceleration of object falling at terminal velocity is also 0 ms-² since it is no longer accelerating.

Simple typical worked problem on Newton’s Second Law (F= ma)

In this video, it provides a simple and typical problem which can be solved by finding resultant force first, and then followed by acceleration. The direction to the right in this problem is chosen to be +ve while to the left is -ve.

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Thus, Resultant force = 250 N — 50 N = 200 N.
Then, using F = ma,
200 = (50) a
a = 4 ms-²
Acceleration of the hockey gear is 4 ms-² to the right since to the right is +ve direction.

Please follow on to some extension questions below not mentioned in the video.

Qn: Is the hockey gear moving with constant velocity?
Ans: Obviously not since there is an acceleration of 4 ms-².

Qn: If the hockey gear later moves at a constant velocity, what will be its acceleration?
Ans: Its acceleration will become 0 ms-².

Qn: What will now be the required forward pulling force to the right to allow this constant velocity to be reached (assuming frictional force to the left is still kept at 50 N)?
Ans: The pulling force will have to be also 50 N but to the right so that the resultant force on the hockey gear is 0 N (Resultant force = 50 — 50 = 0 N) meaning the acceleration is also 0 ms-² since F= ma. Thus, with no acceleration, the hockey gear can now move at constant velocity to the right.

**Note that some students have the misconception that when resultant force is 0 N, the object must always be at rest. In this extension question, it shows us that resultant force is 0 N can also mean that the object may be moving at constant velocity with no acceleration! So, resultant force is 0 N can actually have two possible scenarios (either the object is at rest or moving at constant velocity e.g. in this extension question)!

Explain why a car starting from rest reaches a maximum constant speed when the engine is operating at its maximum power.


As the car starts from rest, the forward driving force is greater than the total resistive forces of friction and air resistance acting against the motion. The car experiences a resultant force in forward direction. Since resultant force = mass X acceleration, the car accelerates and its speed increases.

As the car engine is operating at its maximum power, the car is travelling with a maximum constant forward driving force. The total resistive forces of friction and air resistance increases to oppose motion. The resultant force of car in forward direction decreases. Thus, acceleration of car decreases. The car increases its speed at a decreasing rate.

After sometime, the total resistive forces of friction and air resistance increases until they are equal to the forward maximum constant driving force. The resultant force thus becomes 0 N and there is no net resultant force on the car. Thus, there is no acceleration of the car and it travels with a maximum constant terminal velocity in forward direction.

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Terminal velocity

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The downward force of gravity (Fg) equals the restraining force of drag (Fd) plus the buoyancy. The net force on the object is zero, and the result is that the velocity of the object remains constant.

Terminal velocity is the maximum velocity (speed) attainable by an object as it falls through a fluid (air is the most common example). It occurs when the sum of the drag force (Fd) and the buoyancy is equal to the downward force of gravity (FG) acting on the object. Since the net force on the object is zero, the object has zero acceleration. [1]

In fluid dynamics an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving. [2]

As the speed of an object increases, so does the drag force acting on it, which also depends on the substance it is passing through (for example air or water). At some speed, the drag or force of resistance will equal the gravitational pull on the object (buoyancy is considered below). At this point the object stops accelerating and continues falling at a constant speed called the terminal velocity (also called settling velocity). An object moving downward faster than the terminal velocity (for example because it was thrown downwards, it fell from a thinner part of the atmosphere, or it changed shape) will slow down until it reaches the terminal velocity. Drag depends on the projected area, here represented by the object’s cross-section or silhouette in a horizontal plane. An object with a large projected area relative to its mass, such as a parachute, has a lower terminal velocity than one with a small projected area relative to its mass, such as a dart. In general, for the same shape and material, the terminal velocity of an object increases with size. This is because the downward force (weight) is proportional to the cube of the linear dimension, but the air resistance is approximately proportional to the cross-section area which increases only as the square of the linear dimension. For very small objects such as dust and mist, the terminal velocity is easily overcome by convection currents which can prevent them from reaching the ground at all, and hence they can stay suspended in the air for indefinite periods. Air pollution and fog are examples of convection currents.

Examples [ edit ]

Graph of velocity versus time of a skydiver reaching a terminal velocity.

Based on air resistance, for example, the terminal speed of a skydiver in a belly-to-earth (i.e., face down) free fall position is about 55 m/s (180 ft/s). [3] This speed is the asymptotic limiting value of the speed, and the forces acting on the body balance each other more and more closely as the terminal speed is approached. In this example, a speed of 50% of terminal speed is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on.

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Higher speeds can be attained if the skydiver pulls in their limbs (see also freeflying). In this case, the terminal speed increases to about 90 m/s (300 ft/s), [3] which is almost the terminal speed of the peregrine falcon diving down on its prey. [4] The same terminal speed is reached for a typical .30-06 bullet dropping downwards—when it is returning to the ground having been fired upwards, or dropped from a tower—according to a 1920 U.S. Army Ordnance study. [5]

Competition speed skydivers fly in a head-down position and can reach speeds of 150 m/s (490 ft/s); [ citation needed ] the current record is held by Felix Baumgartner who jumped from an altitude of 38,887 m (127,582 ft) and reached 380 m/s (1,200 ft/s), though he achieved this speed at high altitude where the density of the air is much lower than at the Earth’s surface, producing a correspondingly lower drag force. [6]

The biologist J. B. S. Haldane wrote,

To the mouse and any smaller animal [gravity] presents practically no dangers. You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes. For the resistance presented to movement by the air is proportional to the surface of the moving object. Divide an animal’s length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force. [7]

Physics [ edit ]

Using mathematical terms, terminal speed—without considering buoyancy effects—is given by

V t = 2 m g ρ A C d =>>>>

  • V t > represents terminal velocity,
  • m is the mass of the falling object,
  • g is the acceleration due to gravity,
  • C d > is the drag coefficient,
  • ρ is the density of the fluid through which the object is falling, and
  • A is the projected area of the object. [8]

In reality, an object approaches its terminal speed asymptotically.

Buoyancy effects, due to the upward force on the object by the surrounding fluid, can be taken into account using Archimedes’ principle: the mass m has to be reduced by the displaced fluid mass ρ V , with V the volume of the object. So instead of m use the reduced mass m r = m − ρ V =m-rho V> in this and subsequent formulas.

The terminal speed of an object changes due to the properties of the fluid, the mass of the object and its projected cross-sectional surface area.

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Air density increases with decreasing altitude, at about 1% per 80 metres (260 ft) (see barometric formula). For objects falling through the atmosphere, for every 160 metres (520 ft) of fall, the terminal speed decreases 1%. After reaching the local terminal velocity, while continuing the fall, speed decreases to change with the local terminal speed.

Derivation for terminal velocity [ edit ]

Using mathematical terms, defining down to be positive, the net force acting on an object falling near the surface of Earth is (according to the drag equation):

F net = m a = m g − 1 2 ρ v 2 A C d , >=ma=mg->rho v^AC_,>
with v(t) the velocity of the object as a function of time t.

At equilibrium, the net force is zero (Fnet = 0) [9] and the velocity becomes the terminal velocity limt→∞ v(t) = Vt :

m g − 1 2 ρ V t 2 A C d = 0. rho V_^AC_=0.>

Solving for Vt yields

The Difference Between Terminal Velocity and Free Fall

Sky divers

Dr. Helmenstine holds a Ph.D. in biomedical sciences and is a science writer, educator, and consultant. She has taught science courses at the high school, college, and graduate levels.

Updated on January 24, 2020

Terminal velocity and free fall are two related concepts that tend to get confusing because they depend on whether or not a body is in empty space or in a fluid (e.g., an atmosphere or even water). Take a look at the definitions and equations of the terms, how they are related, and how fast a body falls in free fall or at terminal velocity under different conditions.

Terminal Velocity Definition

Terminal velocity is defined as the highest velocity that can be achieved by an object that is falling through a fluid, such as air or water. When terminal velocity is reached, the downward force of gravity is equal to the sum of the object’s buoyancy and the drag force. An object at terminal velocity has zero net acceleration.

Terminal Velocity Equation

There are two particularly useful equations for finding terminal velocity. The first is for terminal velocity without taking into account buoyancy:

  • Vt is the terminal velocity
  • m is the mass of the object that is falling
  • g is acceleration due to gravity
  • Cd is the drag coefficient
  • ρ is the density of the fluid through which the object is falling
  • A is the cross-sectional area projected by the object

In liquids, in particular, it’s important to account for the buoyancy of the object. Archimedes’ principle is used to account for the displacement of volume (V) by the mass. The equation then becomes:

Free Fall Definition

The everyday use of the term «free fall» is not the same as the scientific definition. In common usage, a skydiver is considered to be in free fall upon achieving terminal velocity without a parachute. In actuality, the weight of the skydiver is supported by a cushion of air.

Freefall is defined either according to Newtonian (classical) physics or in terms of general relativity. In classical mechanics, free fall describes the motion of a body when the only force acting upon it is gravity. The direction of the movement (up, down, etc.) is unimportant. If the gravitational field is uniform, it acts equally on all parts of the body, making it «weightless» or experiencing «0 g». Although it might seem strange, an object can be in free fall even when moving upward or at the top of its motion. A skydiver jumping from outside the atmosphere (like a HALO jump) very nearly achieves true terminal velocity and free fall.

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In general, as long as air resistance is negligible with respect to an object’s weight, it can achieve free fall. Examples include:

  • A spacecraft in space without a propulsion system engaged
  • An object thrown upward
  • An object dropped from a drop tower or into a drop tube
  • A person jumping up

In contrast, objects not in free fall include:

  • A flying bird
  • A flying aircraft (because the wings provide lift)
  • Using a parachute (because it counters gravity with drag and in some cases may provide lift)
  • A skydiver not using a parachute (because the drag force equals his weight at terminal velocity)

In general relativity, free fall is defined as the movement of a body along a geodesic, with gravity described as space-time curvature.

Free Fall Equation

If an object is falling toward the surface of a planet and the force of gravity is much greater than the force of air resistance or else its velocity is much less than terminal velocity, the vertical velocity of free fall may be approximated as:

  • vt is the vertical velocity in meters per second
  • v is the initial velocity (m/s)
  • g is the acceleration due to gravity (about 9.81 m/s 2 near Earth)
  • t is the elapsed time (s)

How Fast Is Terminal Velocity? How Far Do You Fall?

Because terminal velocity depends on drag and an object’s cross-section, there is no one speed for terminal velocity. In general, a person falling through the air on Earth reaches terminal velocity after about 12 seconds, which covers about 450 meters or 1500 feet.

A skydiver in the belly-to-earth position reaches a terminal velocity of about 195 km/hr (54 m/s or 121 mph). If the skydiver pulls in his arms and legs, his cross-section is decreased, increasing terminal velocity to about 320 km/hr (90 m/s or just under 200 mph). This is about the same as the terminal velocity achieved by a peregrine falcon diving for prey or for a bullet falling down after having been dropped or fired upward. The world record terminal velocity was set by Felix Baumgartner, who jumped from 39,000 meters and reached a terminal velocity of 1,341 km/hr (834 mph).

References and Further Reading

  • Huang, Jian. «Speed of a Skydiver (Terminal Velocity)». The Physics Factbook. Glenn Elert, Midwood High School, Brooklyn College, 1999.
  • U.S. Fish and Wildlife Service. «All About the Peregrine Falcon.» December 20, 2007.
  • The Ballistician. «Bullets in the Sky». W. Square Enterprises, 9826 Sagedale, Houston, Texas 77089, March 2001.
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