Elementary Classical Physics 1 Notes Weeks 2 Chapter 2 (cont) 2.3 Acceleration Acceleration­ rate of change in velocity Average acceleration a=Δv/Δt Instantaneous acceleration a=lim Δv/Δt=dv/dt Δt→ 0 Acceleration is the second derivative of position ❑ t¿ 2 2 a=dv/dt=d(dx)/dt(dt)=d (x)/d ¿ Scenarios: 1) Accelerating when a is in same direction as v a) V 1nd V 2re positive and a is positive b) V 1nd V 2re negative and a is negative 2) Decelerating when a is in the opposite direction as v a) V 1nd V 2re positive and a is negative b) V 1nd V 2re negative and a is positive 2.4 Constant Acceleration Where a=a Velocity increases steadily v=v 0at v =x­x 0t­0 v =½ (v 0v) Combine into x=x +0 t01/2at 2 2 Don’t have t in the problem v❑ =v 02a(x­x ) 0 Example 2.3 Example 2.4 2.5 Acceleration of Gravity (1D motion with constant a) 2 All objects experience the same acceleration due to gravity= 9.8 m/s Motion is vertical so we use y instead of x If y is “+” then a= ­g (upward motion) If y is “­” then a= g (downward motion) The equations for constant acceleration apply v=v 0gt y=y +½(v +v)t 0 0 y=y 0v t01/2gt 2 v =v 02g(y­y ) 0 Example 2.6 2.6 When Acceleration isn’t Constant Remember that v