Answer:
1) a = dv / dt , v = v₀ + a t
2) v = dx / dt, x = v₀ t + ½ a t²
Step-by-step explanation:
This is an exercise in kinematics
1) they ask us for the relationship between speed and acceleration
general case
a = dv / dt
constant acceleration case
v = v₀ + a t
these are the mathematical relationships between acceleration and speed, we see that for cases where acceleration is constant the relationship is a straight line, so it is very easy to work, when we have several accelerations in a problem, we define a different range for each and we work as if they were separate problems.
A graphical relationship is the line where the slope is the value of the acceleration.
2) The mathematical relationship between speed and position is
non-constant acceleration case
v = dx / dt
case with zero acceleration
v = x / t
case with nonzero acceleration
x = v₀ t + ½ a t²
we see that for this part we have more possibilities when there is no acceleration the relationship is a straight line and when there is acceleration it is a parabola. Again each interval to work is determined by the value of the acceleration
In a graphical representation we have two possibilities, a line where the slope of the initial velocity and a parabola
3) The angle of inclination affects speed because it has two parts, one on the x-axis and one on the y-axis, each one less than the initial speed. These speeds are given by
vₓ = v₀ cos θ
v_y = v₀ sin θ
and the initial velocity is
