Motion in 1 Dimension

Motion in 1 Dimension

Understanding Motion in One Dimension

  • Motion in one dimension describes the linear movement of an object along a straight line.
  • This movement can be in any direction - horizontal, vertical, or slanted.
  • Two basic concepts in one-dimensional kinematics are distance and displacement. Distance is scalar and only has magnitude, while displacement is vector and has both magnitude and direction.
  • The average speed of an object in motion describes the total distance travelled over a certain time interval, regardless of the direction of the movement.
  • The average velocity, on the other hand, takes into account the displacement from the original position and the time taken. Unlike speed, velocity carries a direction.
  • The instantaneous speed is the speed of an object at a specific instant, obtained by considering an infinitesimally small time interval.
  • The instantaneous velocity is the rate of change of displacement with respect to time at a specific instant.

Applying Kinematic Equations

  • The first equation of motion relates final velocity, initial velocity, acceleration and time: v = u + at, where v is final velocity, u is initial velocity, a is acceleration and t is time.
  • The second equation of motion relates displacement, initial velocity, time and acceleration: s = ut + 1/2at².
  • The third equation of motion relates final velocity, initial velocity, acceleration and displacement: v² = u² + 2as.
  • These equations portray uniform acceleration, meaning the acceleration is constant over the time interval.

Demonstrating Proficiency with Graphs

  • Displacement-time graphs help visualise displacement over time. The gradient of the line in this graph gives the velocity, and the area under the graph gives the displacement.
  • Velocity-time graphs display velocity over time. The gradient gives the acceleration, and the area under the graph gives the displacement.
  • Acceleration-time graphs illustrate an object’s acceleration over time. The area under the graph gives the change in velocity.

Comprehending Relative Velocity

  • Relative velocity describes the velocity of one object relative to another. It depends on the velocity of both the observer and the observed.