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Pavel [41]
3 years ago
7

Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x' (t) is its velocity, and x'

' (t) is its acceleration. x(t) = t3 − 12t2 + 21t − 9, 0 ≤ t ≤ 10 (a) Find the velocity and acceleration of the particle.
Physics
1 answer:
nignag [31]3 years ago
5 0

The position of the particle is given by:

x(t) = t³ - 12t² + 21t - 9

Differentiate x(t) with respect to t to find the velocity x'(t):

x'(t) = 3t² - 24t + 21

Differentiate x'(t) with respect to t to find the acceleration x''(t):

x''(t) = 6t - 24

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noname [10]

The initial velocity of the ball is 1.01 m/s

Explanation:

The motion of the ball rolling off the desk is a projectile motion, which consists of two independent motions:

- A uniform horizontal motion with constant horizontal velocity

- A vertical accelerated motion with constant acceleration (g=9.8 m/s^2, acceleration due to gravity)

We start by analyzing the vertical motion: we can find the time of flight of the ball by using the following suvat equation

s=ut+\frac{1}{2}gt^2

where

s = 1.20 m is the vertical displacement (the height of the desk)

u = 0 is the initial vertical velocity

g=9.8 m/s^2

t is the time of flight

Solving for t,

t=\sqrt{\frac{2s}{g}}=\sqrt{\frac{2(1.20)}{9.8}}=0.495 s

Now we analyze the horizontal motion. We know that the ball covers a horizontal distance of

d = 0.50 m

in a time

t = 0.495 s

Therefore, since the horizontal velocity is constant, we can calculate it as

v_x = \frac{d}{t}=\frac{0.50}{0.495}=1.01 m/s

So, the ball rolls off the table at 1.01 m/s.

Learn more about projectile motion:

brainly.com/question/8751410

#LearnwithBrainly

4 0
3 years ago
A 12 N force is used to pull a wagon 10 m to the left in 15 seconds. Which of the following represents the magnitude of the forc
Lana71 [14]

1. - 12N

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3. - 0.5 m/s/s

7 0
3 years ago
Read 2 more answers
Acceleration always involves a change in
Scrat [10]
Velocity. Since velocity consists of a speed and a direction, acceleration is a change in speed, or direction, or both.
5 0
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-A 180 kg hippo is riding a bicycle at a speed of 6.0
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Answer:

0.0675 seconds

Explanation:

From the question,

We apply newton's second law of motion

F = m(v-u)/t.................... Equation 1

Where F = force exert by the brake, v = final speed, u = initial speed m = mass of the bicycle, t = time.

make t the subject of the equation

t = m(v-u)/F................... Equation 2

Given: m = 180 kg, u = 6.0 m/s, v = 0 m/s (comes to stop), F = -1600 N ( agianst the dirction of motion)

Substitute these value into equation 2

t = 180(0-6.0)/-1600

t = -1080/-1600

t = 0.0675 seconds.

8 0
2 years ago
George created an advertisement for a retail store that sold clothes. He added a discount in the form of a coupon that the custo
likoan [24]

Answer:

The advertisement feature that George can use is a coupon booklet  with the local newspaper for delivery

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George focus on promotion rather than using the other stores strategy of word-of-mouth. Different types of promotion: advertising, public relations, direct selling and sales promotions.A temporary reduction in the price, such as 50% off. Reduction amount  may be a percentage that can be marked on the package.A coupon booklet is inserted into the local newspaper for delivery. Also on checkout  the customer can be given a coupon based on products purchased. The consumer is automatically entered into the contest/event by purchasing the product.

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Consumers get one sample for free, after their trial and then could decide whether to buy or not

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