find the speeds or distance equals to 290 km our time equals to 3 hours. how to solve this diagram and answer
Answers
Answer:
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Step-by-step explanation:
Step-by-step explanation:
Speed is directly proportional to distance when time is constant: v ∝ s (t constant)
Speed is inversely proportional to time when distance is constant: v ∝
1
t
(s constant)
Combining these two rules together gives the definition of speed in symbolic form.
v = s
t
☞ This is not the final definition.
Don't like symbols? Well then, here's another way to define speed. Speed is the rate of change of distance with time.
In order to calculate the speed of an object we must know how far it's gone and how long it took to get there. "Farther" and "sooner" correspond to "faster". Let's say you drove a car from New York to Boston. The distance by road is roughly 300 km (200 miles). If the trip takes four hours, what was your speed? Applying the formula above gives…
v = s ≈ 300 km = 75 km/h
t 4 hour
This is the answer the equation gives us, but how right is it? Was 75 kph the speed of the car? Yes, of course it was… Well, maybe, I guess… No, it couldn't have been the speed. Unless you live in a world where cars have some kind of exceptional cruise control and traffic flows in some ideal manner, your speed during this hypothetical journey must certainly have varied. Thus, the number calculated above is not the speed of the car, it's the average speed for the entire journey. In order to emphasize this point, the equation is sometimes modified as follows…
v = ∆s
∆t
The bar over the v indicates an average or a mean and the ∆ (delta) symbol indicates a change. Read it as "vee bar is delta vee over delta tee". This is the quantity we calculated for our hypothetical trip.
In contrast, a car's speedometer shows its instantaneous speed, that is, the speed determined over a very small interval of time — an instant. Ideally this interval should be as close to zero as possible, but in reality we are limited by the sensitivity of our measuring devices. Mentally, however, it is possible to imagine calculating average speed over ever smaller time intervals until we have effectively calculated instantaneous speed. This idea is written symbolically as…
v =
lim
∆t→0
∆s = ds
∆t dt
or, in the language of calculus speed is the first derivative of distance with respect to time.
If you haven't dealt with calculus, don't sweat this definition too much. There are other, simpler ways to find the instantaneous speed of a moving object. On a distance-time graph, speed corresponds to slope and thus the instantaneous speed of an object with non-constant speed can be found from the slope of a line tangent to its curve. We'll deal with that later in this book.
velocity
In order to calculate the speed of an object we need to know how far it's gone and how long it took to get there. A wise person would then ask…
What do you mean by how far? Do you want the distance or the displacement?
A wise person, once upon a time
Your choice of answer to this question determines what you calculate — speed or velocity.
Average speed is the rate of change of distance with time.
Average velocity is the rate of change of displacement with time.
And for the calculus people out there…
Instantaneous speed is the first derivative of distance with respect to time.
Instantaneous velocity is the first derivative of displacement with respect to time.
Speed and velocity are related in much the same way that distance and displacement are related. Speed is a scalar and velocity is a vector. Speed gets the symbol v (italic) and velocity gets the symbol v (boldface). Average values get a bar over the symbol.
average
speed
v = ∆s
∆t
instantaneous
speed
v =
lim
∆t→0
∆s = ds
∆t dt
average
velocity
v = ∆s
∆t
instantaneous
velocity
v =
lim
∆t→0
∆s = ds
∆t dt
Displacement is measured along the shortest path between two points and its magnitude is always less than or equal to the distance. The magnitude of displacement approaches distance as distance approaches zero. That is, distance and displacement are effectively the same (have the same magnitude) when the interval examined is "small". Since speed is based on distance and velocity is based on displacement, these two quantities are effectively the same (have the same magnitude) when the time interval is "small" or, in the language of calculus, the magnitude of an object's average velocity approaches its average speed as the time interval approaches zero.
∆t → 0 ⇒ v → |v|
The instantaneous speed of an object is then the magnitude of its instantaneous velocity.
v = |v|
Speed tells you how fast. Velocity tells you how fast and in what direction.