All categories

3 years ago

Two particles are moving with positions given by x= 4t^2−2t and x= 6t^3+8t respectively.

Physics

1 answer:

Evgen [1.6K]3 years ago

6 0

Explanation:

a)Which of the two has uniform acceleration?

Acceleration is the second derivative of position. The acceleration of the first particle is:

x = 4t² − 2t

v = 8t − 2

a = 8

The acceleration of the second particle is:

x = 6t³ + 8t

v = 18t² + 8

a = 36t

The first particle has uniform acceleration.

b)Which one is likely to come to rest at some time during its motion?

The particles come to rest when v = 0. The first particle's velocity has a real zero at t = 4. The second particle's velocity has only imaginary zeros, meaning v is never 0.

You might be interested in

A body with a mass of 2,000 kg is lifted to a height of 15 m within a time of 15 s. Which one of the following statements concer

Aleksandr [31]

So we want to know which statement is true for the body of mass m=2000kg that is lifted to a height of h=15m in t=15 s. Lets calculate each of the following: Gravity force on the body is F=m*g=2000*9.81=19620 N so a is FALSE. Potential energy of the body when it is lifted to the height of 15 m is Ep=m*g*h=2000*9.81*15=294300 J so b is FALSE. Work to lift the body is: W=Fg*h=2000*9.81*15= Ep=294300 J so c is FALSE. Power P=W/t=294300/15=19620 W So d is TRUE.

8 0

2 years ago

The 8.00-cm long second hand on a watch rotates smoothly.

dolphi86 [110]

The watch hand covers an angular displacement of 2π radians in 60 seconds.

ω = 2π/60
ω = 0.1 rad/s

v = ωr
v = 0.1 x 0.08
v = 8 x 10⁻³ m/s

4 0

3 years ago

The Reynolds number, rho VD/mu, is a very important parameter in fluid mechanics. Verify that the Reynolds number is dimensionle

Agata [3.3K]

Answer:

Re = 1 10⁴

Explanation:

Reynolds number is

Re = ρ v D /μ

The units of each term are

ρ = [kg / m³]

v = [m / s]

D = [m]

μ = [Pa s]

The pressure

Pa = [N / m²] = [Kg m / s²] 1 / [m²] = [kg / m s²]

μ = [Pa s] = [kg / m s²] [s] = [kg / m s]

We substitute the units in the equation

Re = [kg / m³] [m / s] [m] / [kg / m s]

Re = [kg / m s] / [m s / kg]

RE = [ ]

Reynolds number is a scalar

Let's evaluate for the given point

Where the data for methane are:

viscosity μ = 11.2 10⁻⁶ Pa s

the density ρ = 0.656 kg / m³

D = 2 in (2.54 10⁻² m / 1 in) = 5.08 10⁻² m

Re = 0.656 4 2 5.08 10⁻² /11.2 10⁻⁶

Re = 1.19 10⁴

4 0

3 years ago

A ball is thrown vertically upwards from the edge of the cliff and hits the ground at the base of the cliff with a speed of 30 m

olya-2409 [2.1K]

To solve this problem we will apply the linear motion kinematic equations. From the definition of the final velocity, as the sum between the initial velocity and the product between the acceleration (gravity) by time, we will find the final velocity. From the second law of kinematics, we will find the vertical position traveled.

$v = v_0 -gt$