Motion in a Straight Line Quiz

Motion in a Straight Line

Velocity-Displacement

• Velocity: the rate of change of displacement with respect to time
• Displacement: the shortest distance between the initial and final positions of an object
• Equations of motion:
  • v = u + at (where v is final velocity, u is initial velocity, a is acceleration, and t is time)
  • s = ut + (1/2)at^2 (where s is displacement, u is initial velocity, a is acceleration, and t is time)
  • v^2 = u^2 + 2as (where v is final velocity, u is initial velocity, a is acceleration, and s is displacement)

Acceleration-Displacement

• Acceleration: the rate of change of velocity with respect to time
• Acceleration-displacement graph:
  • Acceleration is the slope of the velocity-time graph
  • Displacement is the area under the velocity-time graph
• Relationship between acceleration and displacement:
  • a = Δv / Δt (where a is acceleration, Δv is change in velocity, and Δt is change in time)
  • s = (v1 + v2) / 2 × t (where s is displacement, v1 and v2 are initial and final velocities, and t is time)

Calculus-Based

• Instantaneous velocity: the velocity of an object at a specific instant of time
• Instantaneous acceleration: the acceleration of an object at a specific instant of time
• Derivatives:
  • Velocity is the first derivative of displacement with respect to time (v = ds/dt)
  • Acceleration is the first derivative of velocity with respect to time (a = dv/dt)
  • Acceleration is the second derivative of displacement with respect to time (a = d^2s/dt^2)
• Integration:
  • Displacement can be found by integrating velocity with respect to time (s = ∫v dt)
  • Velocity can be found by integrating acceleration with respect to time (v = ∫a dt)