Chapter 2: Kinematics in One Dimension

Chapter 2 Kinematics in One Dimension

• 2.1 Uniform Motion

• 2.2 Instantaneous Velocity

• 2.3 Finding Position from Velocity

• 2.4 Motion with Constant Acceleration

• 2.5 Free Fall

• 2.6 Motion on an Inclined Plane

• 2.7 Instantaneous Acceleration

Uniform Motion

• Average velocity: $v<em>{ave} ≡ \frac{∆s}{∆t} = \frac{s</em>f - s<em>i}{t</em>f - t_i}$

• Uniform motion: constant velocity.

• Velocity from slope of position-versus-time graph.

• Speed: $v = |v_s|$.

Instantaneous Velocity

• Instantaneous velocity: velocity at a single instant of time.

• $v<em>s ≡ \lim</em>{∆t→0} \frac{∆s}{∆t} = \frac{ds}{dt}$

• Instantaneous velocity at time $t$ is the slope of the tangent to the position-versus-time graph at $t$.

• Turning point: object reverses direction; instantaneous velocity is zero.

Finding Position from Velocity

• Displacement: $∆s = v_{ave}∆t$

• Total displacement from the area under the velocity-versus-time graph.

Motion with Constant Acceleration

• Constant acceleration: $a<em>{ave} = a</em>s$.

• $a<em>{ave} = a</em>s = \frac{∆v<em>s}{∆t} = \frac{v</em>{ff} - v_{ii}}{∆t}$

• $v<em>{ff} = v</em>{ii} + a ∆t$

• $s<em>f = s</em>i + v<em>{ii}∆t + \frac{1}{2}a</em>s ∆t^2$

Free Fall

• Motion under gravity only.

• Acceleration is the same for all objects, regardless of mass.

• Free-fall acceleration: $g = 9.80 m/s^2$

• In conventional coordinate system, $a = -g = -9.80 m/s^2$

Motion on an Inclined Plane

• Constant acceleration: $a_s = ±g sin θ$

Instantaneous Acceleration

• $a<em>s = \frac{dv</em>s}{dt}$

• Instantaneous acceleration at time $t$ is the slope of the tangent to the velocity-versus-time graph at $t$.