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(credit: Wikipedia: Orders of Magnitude (acceleration))
Typical values of acceleration
Acceleration Value (m/s 2 )
High-speed train 0.25
Elevator 2
Cheetah 5
Object in a free fall without air resistance near the surface of Earth 9.8
Space shuttle maximum during launch 29
Parachutist peak during normal opening of parachute 59
F16 aircraft pulling out of a dive 79
Explosive seat ejection from aircraft 147
Sprint missile 982
Fastest rocket sled peak acceleration 1540
Jumping flea 3200
Baseball struck by a bat 30,000
Closing jaws of a trap-jaw ant 1,000,000
Proton in the large Hadron collider 1.9 × 10 9

In this table, we see that typical accelerations vary widely with different objects and have nothing to do with object size or how massive it is. Acceleration can also vary widely with time during the motion of an object. A drag racer has a large acceleration just after its start, but then it tapers off as the vehicle reaches a constant velocity. Its average acceleration can be quite different from its instantaneous acceleration at a particular time during its motion. [link] compares graphically average acceleration with instantaneous acceleration for two very different motions.

Graph A shows acceleration in meters per second squared plotted versus time in seconds. Acceleration varies only slightly and is always in the same direction, since it is positive. The average over the interval is nearly the same as the acceleration at any given time. Graph B shows acceleration in meters per second squared plotted versus time in seconds. Acceleration varies greatly: from -4 meters per second squared to 5 meters per second squared.
Graphs of instantaneous acceleration versus time for two different one-dimensional motions. (a) Acceleration varies only slightly and is always in the same direction, since it is positive. The average over the interval is nearly the same as the acceleration at any given time. (b) Acceleration varies greatly, perhaps representing a package on a post office conveyor belt that is accelerated forward and backward as it bumps along. It is necessary to consider small time intervals (such as from 0–1.0 s) with constant or nearly constant acceleration in such a situation.

Learn about position, velocity, and acceleration graphs. Move the little man back and forth with a mouse and plot his motion. Set the position, velocity, or acceleration and let the simulation move the man for you. Visit this link to use the moving man simulation.

Summary

  • Acceleration is the rate at which velocity changes. Acceleration is a vector; it has both a magnitude and direction. The SI unit for acceleration is meters per second squared.
  • Acceleration can be caused by a change in the magnitude or the direction of the velocity, or both.
  • Instantaneous acceleration a ( t ) is a continuous function of time and gives the acceleration at any specific time during the motion. It is calculated from the derivative of the velocity function. Instantaneous acceleration is the slope of the velocity-versus-time graph.
  • Negative acceleration (sometimes called deceleration) is acceleration in the negative direction in the chosen coordinate system.

Conceptual questions

Is it possible for speed to be constant while acceleration is not zero?

No, in one dimension constant speed requires zero acceleration.

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Is it possible for velocity to be constant while acceleration is not zero? Explain.

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Give an example in which velocity is zero yet acceleration is not.

A ball is thrown into the air and its velocity is zero at the apex of the throw, but acceleration is not zero.

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If a subway train is moving to the left (has a negative velocity) and then comes to a stop, what is the direction of its acceleration? Is the acceleration positive or negative?

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Plus and minus signs are used in one-dimensional motion to indicate direction. What is the sign of an acceleration that reduces the magnitude of a negative velocity? Of a positive velocity?

Plus, minus

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A cheetah can accelerate from rest to a speed of 30.0 m/s in 7.00 s. What is its acceleration?

a = 4.29 m/s 2

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Dr. John Paul Stapp was a U.S. Air Force officer who studied the effects of extreme acceleration on the human body. On December 10, 1954, Stapp rode a rocket sled, accelerating from rest to a top speed of 282 m/s (1015 km/h) in 5.00 s and was brought jarringly back to rest in only 1.40 s. Calculate his (a) acceleration in his direction of motion and (b) acceleration opposite to his direction of motion. Express each in multiples of g (9.80 m/s 2 ) by taking its ratio to the acceleration of gravity.

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Sketch the acceleration-versus-time graph from the following velocity-versus-time graph.

Graph shows velocity in meters per second plotted versus time in seconds. Velocity is zero and zero seconds, increases to 6 meters per second at 20 seconds, decreases to 2 meters per second at 50 and remains constant until 70 seconds, increases to 4 meters per second at 90 seconds, and decreases to –2 meters per second at 100 seconds.

Graph shows acceleration in meters per second squared plotted versus time in seconds. Acceleration is 0.3 meters per second squared between 0 and 20 seconds, -0.1 meters per second squared between 20 and 50 seconds, zero between 50 and 70 seconds, -0.6 between 90 and 100 seconds.

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A commuter backs her car out of her garage with an acceleration of 1.40 m/s 2 . (a) How long does it take her to reach a speed of 2.00 m/s? (b) If she then brakes to a stop in 0.800 s, what is her acceleration?

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Assume an intercontinental ballistic missile goes from rest to a suborbital speed of 6.50 km/s in 60.0 s (the actual speed and time are classified). What is its average acceleration in meters per second and in multiples of g (9.80 m/s 2 )?

a = 11.1 g

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An airplane, starting from rest, moves down the runway at constant acceleration for 18 s and then takes off at a speed of 60 m/s. What is the average acceleration of the plane?

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Practice Key Terms 2

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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