Formula for instantaneous speed?
lim as h->0 of (f(x+h) - f(x))/h
lim as x->a of (f(x) - f(a))/(x - a)
Instantaneous speed is your speed in a given moment. The speedometer in your car and the radar gun that cops use both give a value in instantaneous speed. The disctinction here is to not confuse instantaneous speed with average speed, which is calculated over a set distance. To calculate average speed (V) you need to divide the distance travelled (D) by the time of travel (T). V= D/T
Instantaneous speed: The speed at which I'm moving right now, this instant. Average speed: (The distance I covered during some period of time) divided by (the length of time). I may have had different instantaneous speeds at different points during that time. Acceleration: The rate at which speed changes. Acceleration can also be instantaneous or average over a period of time.
Can the distance traveled still be divided by the time taken to travel the distance if the speed accelerates to travel the distance?
The formula, distance = speed x time, or speed = distance / time, assumes constant speed. If the speed changes, then the formula speed = distance / time will give you the average speed over the time period. To get the instantaneous speed in this case, you must divide distance / time for a very short time interval.
Speed has only size. Velocity has size and direction. If three drivers are driving their cars at 50 mph headed north, 50 mph headed south, and 50 mph headed east, their speeds are all equal, but their velocites are all different. Instantaneous speed is the speed at an instant in time. A point on the edge of an LP record has the same instantaneous speed whenever you look at it. Instantaneous velocity is the velocity…
To be pedantic... In a car with a digital speedometer, speed is NOT instantaneous in the sense that it is a measure of distance per unit time. It does this by measuring a change in distance over a very short period of time to *approximate* the instantaneous speed. If the time period is a small fraction of a second you wouldn't know the difference! For older cars with analog speedometers the speed is instantaneous as…