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11Alexandr11 [23.1K]
2 years ago
10

A ball that rolls on the ground is initially propelled with a speed of 45 km / h and after 10 seconds it stops. Assuming you los

t speed constantly, then: a) Calculate the acceleration b) Calculate the distance traveled.
Physics
1 answer:
solmaris [256]2 years ago
5 0

Answer:

a) -1.25 m/s²

b) 62.5 m

Explanation:

Convert km/h to m/s:

45 km/h × (1000 m/km) × (1 h / 3600 s) = 12.5 m/s

a = Δv / Δt

a = (0 m/s − 12.5 m/s) / 10 s

a = -1.25 m/s²

Δx = ½ (v + v₀) t

Δx = ½ (0 m/s + 12.5 m/s) (10 s)

Δx = 62.5 m

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A billiard ball is dropped from a height of 64 feet. Use the position function s(t) = –16???? 2 + ????0???? + ????0 to answer th
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Answer:

s(t) = -16*t^2 + 64

v(t) = -32*t

a(t) = -32 ft/s^2

v(t) = 64 ft/s ... At impact

Explanation:

Given:-

- The height of the billiard ball t = 0 , h = 64 ft.

- The position function of an object under gravity is given by:

                                    s(t) = -16*t^2 + v_o*t + s_o

Find:-

a. Determine the position function s(t),

b. the velocity function v(t),

c. the acceleration function a(t).

d. What is the velocity of the ball at impact?

Solution:-

- To determine the position function we must initialize our problem and use the given general equation.

- s(t) is the position of the billiard ball from the ground at time t. So when t = 0, then s(t) = h. Hence, we have:

                                  s(t) = s_o = h = 64 ft

- Similarly we know that v_o is the initial velocity of the ball. Since, the ball was dropped we say that the initial velocity v_o = 0. Hence, the position of the ball from ground is given by following expression:

                                  s(t) = -16*t^2 + 64  

- To find the velocity expression v(t) we will take the time derivative of the position expression s(t) as follows:

                                  v(t) = d s(t) / dt

                                  v(t) = -16*2*t + 0

                                  v(t) = -32*t ft/s

- Similarly, the expression for acceleration a(t) is given by the time derivative of the velocity expression v(t) as follows:

                                  a(t) = d v(t) / dt

                                  a(t) = -32*t

                                  a(t) = -32 ft/s^2

- The velocity of ball at impact can be determined by evaluating s(t) = 0 and find the value for time t. Then that time t can be substituted in the velocity expression v(t) for final velocity. Or we could use the following 3rd kinematic equation as follows:

                                 v(t)^2 - 0^2 = 2*a(t)*s_o

                                 v(t)^2 = 2*(32)*(64)

                                 v(t) = 64 ft/s

- The ball has a velocity of 64 ft/s at impact!

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What is the difference between the equilibrium vector and the resultant vector
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Answer:

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From the question we are told that

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Generally the frictional force that acts on the puck is mathematically represented as

          F_f =  \mu_k  *  F_N

=>       F_f =  0.35  *  5

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