Question

a)How can you prove that ;Where an object has
a steady speed, the slope of the distance–time graph
is constant, and the object’s average speed and its
instantaneous speed are the same

b)What does this statement mean;The three laws of motion allow us to
calculate accurately the motion of any object over time
and in three dimensions.

Answer 1

if you have a distance-time graph x(t), what does the derivative x'(t) represent?

Answer 2

It represents instaneous speed

Answer 3

at a particular point

Answer 4

right, and if it says that speed is constant, then \(x'(t)=v(t)=C\) where \(C\) is some constant
therefor we can get some function for \(x(t)\) by integrating \[x(t)=\int v(t)dt=\int C dt\]and what do you get by doing that integral?

Answer 5

distance

Answer 6

you get the distance function x(t), which after doing the integral you find is....?

Answer 7

from a to b
average velocity is this: -