Acceleration and Distance-Time Graph for Uniform Motion

Acceleration Principles and Formulas

  • Real-World Example of Variable Motion:
    • On a park slide, an object's velocity is less at the top.
    • The velocity increases while sliding down the middle section.
    • The velocity becomes 00 towards the end of the slide.
  • Definition of Acceleration:
    • Acceleration is defined as the rate of change of velocity.
    • Acceleration=Change in velocityTime\text{Acceleration} = \frac{\text{Change in velocity}}{\text{Time}}
  • Mathematical Formula for Acceleration:
    • Let initial velocity be represented by uu.
    • Let final velocity after time interval tt be represented by vv.
    • Let acceleration be represented by aa.
    • Acceleration=a=Final velocity−Initial velocityTime\text{Acceleration} = a = \frac{\text{Final velocity} - \text{Initial velocity}}{\text{Time}}
    • a=v−uta = \frac{v - u}{t}

Motion Conditions and Special Values

  • Accelerated Motion:
    • An object undergoes accelerated motion if its velocity changes during a given time period.
  • Velocity Conditions at Rest:
    • When an object is at rest at the beginning of its motion, its initial velocity is u=0u = 0
    • When an object comes to rest at the end of its motion, its final velocity is v=0v = 0

Categorization of Acceleration

  • Uniform Acceleration:
    • If the velocity of an object changes by equal amounts in equal time intervals, the object is in uniform acceleration.
  • Non-Uniform Acceleration:
    • If the velocity of an object changes by unequal amounts in equal time intervals, the object is in non-uniform acceleration.
  • Directional and Quantitative Types of Acceleration:
    • Positive Acceleration:
    • Occurs when the velocity of an object increases with time.
    • The direction of positive acceleration is in the direction of velocity.
    • Negative Acceleration (Deceleration):
    • Occurs when the velocity of an object decreases with time.
    • Negative acceleration is also referred to as deceleration.
    • The direction of negative acceleration is opposite to the direction of velocity.
    • Zero Acceleration:
    • Occurs if the velocity of the object does not change with time.

Distance-Time Graph for Uniform Motion

  • Quantitative Motion Data of a Car over Fixed Time Intervals:
    • At time t=0 secondst = 0\text{ seconds}, distance covered d=0 metresd = 0\text{ metres}
    • At time t=10 secondst = 10\text{ seconds}, distance covered d=15 metresd = 15\text{ metres}
    • At time t=20 secondst = 20\text{ seconds}, distance covered d=30 metresd = 30\text{ metres}
    • At time t=30 secondst = 30\text{ seconds}, distance covered d=45 metresd = 45\text{ metres}
    • At time t=40 secondst = 40\text{ seconds}, distance covered d=60 metresd = 60\text{ metres}
    • At time t=50 secondst = 50\text{ seconds}, distance covered d=75 metresd = 75\text{ metres}
    • At time t=60 secondst = 60\text{ seconds}, distance covered d=90 metresd = 90\text{ metres}
    • At time t=70 secondst = 70\text{ seconds}, distance covered d=105 metresd = 105\text{ metres}
  • Graph Construction Parameters:
    • Plot time along the X-axis.
    • Plot distance along the Y-axis.
    • X-axis Scale: 1 cm=10 seconds1\text{ cm} = 10\text{ seconds}
    • Y-axis Scale: 1 cm=20 metres1\text{ cm} = 20\text{ metres}

Distance - time graph for uniform motion