Instantaneous Velocity 2.2

In certain cases, as physicists, we want to solve a problem that deals with a speed at a certain time in space. This is instantaneous velocity. Remember this is only along a straight path. Later we will deal with more complex examples.

As the change in x and the change in t(time) become extremely close to each other. In terms of calculus, we would say the limit of delta x over delta t is our derivative x with respect to t, which is written at dx/dt. 

The time interval, we must remember, is always positive. Instantaneous velocity is a vector quantity. One other thing a physics student should know is the difference between speed and instantaneous velocity. Speed measures how fast something is moving. Instantaneous velocity is the measure of how fast and what direction a particle is moving.

Another part of instantaneous speed is that it does not matter whether or not the velocity of something is negative or positive. For example, lets say a particle is moving at a rate of -67 m/s and another is moving at 67 m/s. The instantaneous speed is still 67 m/s

Lets do a problem from the book University Physics

A cheetah is crouched 20 m to the east of an observer . At time t = 0 the cheetah begins to run due east toward an antelope that is 50 m to the east of the observer. During the first 2.0 s of the attack, the cheetah’s coordinate x varies with time according to the equation x = 20 m + 15.0 m>s22t2. (a) Find the cheetah’s displacement between t1 = 1.0 s and t2 = 2.0 s. (b) Find its average velocity during that interval. (c) Find its instantaneous velocity at t1 = 1.0 s by taking ¢t = 0.1 s, then 0.01 s, then 0.001 s. (d) Derive an expression for the cheetah’s instantaneous velocity as a function of time, and use it to find vx at t = 1.0 s and t = 2.0 s. 

We will revisit this problem tomorrow(7/23)

Mark Jackson