Overview
This lecture explains the differences between average and instantaneous speed, velocity, and acceleration, with examples and problem-solving steps in straight-line motion.
Average and Instantaneous Speed
- Average speed is a scalar showing the rate of distance covered; calculated as distance divided by time.
- The formula for average speed is: average speed = total distance / total time.
- The unit for average speed is meters per second (m/s).
- Instantaneous speed is how fast an object moves at a specific moment; it has no duration and cannot be negative.
Average and Instantaneous Velocity
- Average velocity is a vector showing the rate of change of position; calculated as displacement divided by time.
- The formula for average velocity is: average velocity = (x₂ - x₁) / time, where x is position.
- The unit for average velocity is meters per second (m/s).
- Instantaneous velocity is the velocity at a single instant; it’s the limit of average velocity as the time interval approaches zero.
- A positive instantaneous velocity means motion in the positive x direction, negative means motion in the negative x direction.
- Instantaneous speed is the magnitude of instantaneous velocity.
Average and Instantaneous Acceleration
- Average acceleration is a vector: change in velocity divided by time interval.
- The formula is: average acceleration = (v_final - v_initial) / (t_final - t_initial).
- Instantaneous acceleration is the limit of average acceleration as the time interval approaches zero and is found by taking the derivative of velocity with respect to time.
Example Problems
- For v = 40 - 5t² (velocity in m/s, t in s), average acceleration from t=0 to t=2 is (20 - 40) / (2 - 0) = -10 m/s².
- For v = 40 + 0.5t², instantaneous acceleration is the derivative: a = 1.0t; at t = 3 s, a = 3 m/s².
Quiz Review
- Question: Which bodies move with constant speed? Answer is (b) 1 and 4 only.
Key Terms & Definitions
- Scalar — a quantity with magnitude only.
- Vector — a quantity with both magnitude and direction.
- Average speed — total distance divided by total time.
- Average velocity — total displacement divided by total time.
- Instantaneous speed — speed at a particular instant (always positive).
- Instantaneous velocity — velocity at a particular instant, includes direction.
- Average acceleration — change in velocity divided by change in time.
- Instantaneous acceleration — rate of change of velocity at a particular instant.
Action Items / Next Steps
- Prepare for the next lesson on graphs in straight-line motion.
- Review definitions and formulas for speed, velocity, and acceleration.
- Practice solving similar problems from the lecture.