Velocity and acceleration. Speed is a scalar Note: Speed is always positive. avg is short for average 平均.

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Presentation transcript:

Velocity and acceleration

Speed is a scalar Note: Speed is always positive. avg is short for average 平均

1400 km What is the distance traveled in meters? The flight took 2 hours and 20 minutes. What is this in seconds?

Velocity is a vector Units: m/s 速度

Velocity is a vector Remember: Δ is the Greek letter Delta, and means ‘change in something’.

Dimensions on both sides must match

1400 km x y

Calculating a unit vector from angles where θ is the angle between the vector and the relevant axis.

Instantaneous velocity Our first use of calculus. 微积分瞬时

Instantaneous velocity “the derivative of r with respect to t” 导数

Instantaneous velocity “the rate of change of r”

The derivative of a vector is actually three derivatives

A reminder…

What is the solution to ? (1) (2) (3) (4) (5)

Acceleration: rate of change of velocity 加速度 Units: m/s 2

Acceleration: rate of change of velocity Average acceleration: Instantaneous acceleration:

Bumper car ride

Example: The position of a bumper car is described as a function of time by: Find: (a) The displacement and average velocity between t = 1.0 s and t = 3.0 s.

Bumper car ride Example: The position of a bumper car is described as a function of time by: Find: (b) The instantaneous velocity of the car at t = 3.0 s.

Bumper car ride Example: The position of a bumper car is described as a function of time by: Find: (c) The instantaneous acceleration of the car at t = 3.0 s.