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Negative Acceleration: Definition, Formula, and Examples

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Negative acceleration is the process of slowing down an object’s speed or velocity. It happens when an object is moving in a particular direction and its speed decreases over time.
Negative acceleration is also known as deceleration and is measured in meters per second squared (m/s²).
For instance, when a car brakes to stop, it undergoes negative acceleration as its speed decreases.
The formula for negative acceleration is:

a = (v2 – v1) / t

where:

  • a is the negative acceleration;
  • v2 is the initial velocity;
  • v1 is the final velocity;
  • t is the time taken for the object to slow down.

Daily Life Examples of Negative Acceleration

  1. A car coming to a stop at a red traffic light.
  2. An elevator slowing down before it reaches a floor.
  3. A person jumping from a trampoline and coming to a stop on the ground.
  4. A bicycle slowing down when the brakes are applied.
  5. A person slowing down while running and coming to a stop.
  6. A rollercoaster coming to a stop at the end of the ride.
  7. A basketball player jumping up to dunk the ball and then landing on the ground.
  8. A child on a swing slowing down and coming to a stop.

Different Cases of Negative Acceleration

ExampleInitial VelocityFinal VelocityTimeAcceleration FormulaAcceleration Value
Car slowing down60 mph40 mph5 secondsa = (v_f – v_i) / t-4 mph/s
Runner stopping10 m/s0 m/s2 secondsa = (v_f – v_i) / t-5 m/s^2
Train stopping50 km/h0 km/h20 secondsa = (v_f – v_i) / t-2.5 km/h^2
RollercoasterVariesVariesVariesa = (v_f – v_i) / tVaries

Multiple Choice Questions

  1. Which of the following is a synonym for negative acceleration?
    A) Acceleration due to gravity
    B) Retardation
    C) Velocity increase
    D) Kinetic energy

Answer: B) Retardation

  1. An object has an initial velocity of 20 m/s and comes to a stop in 10 seconds. What is its acceleration?
    A) -2 m/s^2
    B) -4 m/s^2
    C) -6 m/s^2
    D) -8 m/s^2

Answer: A) -2 m/s^2

  1. Which of the following is an example of negative acceleration?
    A) A ball rolling down a hill
    B) A rocket launching into space
    C) A car driving at a constant speed on a straight road
    D) A person jumping off a diving board

Answer: D) A person jumping off a diving board

  1. A car is traveling at 50 mph and comes to a stop in 5 seconds. What is its acceleration?
    A) -5 mph/s
    B) -10 mph/s
    C) -15 mph/s
    D) -20 mph/s

Answer: D) -20 mph/s

  1. Which of the following is the correct formula for acceleration?
    A) a = v_f / t
    B) a = v_i / t
    C) a = (v_f – v_i) / t
    D) a = m * g

Answer: C) a = (v_f – v_i) / t

More Links

SI Unit of Work| Definition, Formula, and Examples

Uniform Circular Motion| Real-Life Examples

Linear Motion or Rectilinear Motion| Daily Life Examples

Kinematic Equations| Sample Problems and Solutions

Linear Acceleration

Umair Javaid, PhD Student
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