An object which starts at the origin is traveling in the positive direction with a constant velocity V. After traveling a distan

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An object which starts at the origin is traveling in the positive direction with a constant velocity V. After traveling a distan

ce D with this constant velocity, the object begins to slow down at a constant rate until it stops after traveling an addition distance of 2D. In terms of D and V, determine the average velocity of the entire trip.

Physics

2 answers:

zepelin [54] · Answer 1 · 2022-09-07T04:18:58+03:00

With the concept of kinematics we find the average speed is 0.6V

given parameters

* initial velocity V

* the distances in each part of the movements x₁ = D and x₂ = 2D

to find

The average speed of the entire trajectory

In kinematics we analyze the motion of bodies, the average velocity is defined by

$V_{avg} = \frac{\Delta x}{\Delta t}$ 1

where $V_{avg}$ is the average velocity, Δx and Δt are the variation of displacement and time in the interval

For this exercise we have two types of movement in the first part a uniform movement and in the second part an accelerated movement let's solve each onaccelerated movement,e separately

1 Part. uniform motion

we look for the time

V = $\frac{x_1}{t_1}$

t₁ = x₁ / V

t₁ = $\frac{D}{V}$

2 Part. Accelerated movement, let's start by looking for acceleration, they tell us that the body stops at the end of the interval so its velocity is zero v_f=0, the initial velocity is v₀ = V

$v_f^2 = v_o^2 - 2 \ a \ x_2$

0 = v₀² - 2 a x₂

a = $\frac{v_o^2}{2x_2}$

we substitute

a = $\frac{V^2}{D}$

now we look for the time it takes to stop

v = v₀ - a t₂

0 = v₀ - a t₂

t₂ = $\frac{v_o}{a}$

we substitute

t₂ = $\frac{V}{\frac{V^2}{4D} }$

t₂ = $\frac{4D}{V}$ 4D / V

for the entire movement, the total displacement is

Δx = x₁ + x₂

Δx = D + 2D

Δx = 3D

the total time is

Δt = t₁ + t₂

Δt = $\frac{D}{V} + \frac{4D}{V}$

Δt = $\frac{5D}{V}$

we substitute in equation 1 of average velocity

$V_{avg} = \frac{3D}{\frac{5D}{V} }$

$V_{avg} = \frac{3}{5} \ V$

$V_{avg } = 0.6 V$

With the use of the kinematics equations with constant acceleration we can find the average velocity of the body throughout the journey is 0.6V

learn more about average speed here:

brainly.com/question/11265533