Acceleration Notes

Acceleration

• Acceleration depends on:

  • Initial velocity
  • Final velocity
  • Time interval over which velocity changes

• Equation:

  • $acceleration = {\Delta V \over \Delta T}$
  • Where $\Delta V$ is the change in velocity and $\Delta T$ is the change in time.

• Delta V:

  • ${\Delta V} = Final Velocity - Initial Velocity$

• Delta T:

  • ${\Delta T} = Final Time - Initial Time$
  • Often the delta is left off of time because time cannot be negative.

• Units for Acceleration:

  • Meters per second squared ($m/s^2$).
  • This means the velocity is changing x meters per second each second that passes.

Example Problem: Race Car Acceleration

• Problem: A race car moving west speeds up from 17 m/s to 47 m/s in 2 seconds. What is the car's acceleration?

• Given Information:

  • Initial Velocity ($V_i$) = 17 m/s
  • Final Velocity ($V_f$) = 47 m/s
  • Time (t) = 2 seconds

• Solution:

  • Using the formula: $acceleration = {\Delta V \over \Delta T}$
  • Plugging in the values: $acceleration = {{47 m/s - 17 m/s} \over {2 s}}$
  • Calculating: $acceleration = {{30 m/s} \over {2 s}}$
  • Final Answer: $acceleration = 15 m/s^2$
  • The car is accelerating at 15 meters per second squared.