Amazon Echo Dot (3rd Gen) - Smart speaker with Alexa

1. 

Convert 1Km to meters 

1 km = 1000 m 

Time = Distance/ Speed 

Time = 1000 m/ 25 m/s = 40 s 

2. 

1 minute = 60 s 

10 minutes = 60 s * 10 = 600 s 

Distance = Speed * Time 

Distance = 20 m/s * 600 s = 12000 m 

1 km = 1000 m 

12000 m = 12000/1000 = 12 Km 

3. 

Echo means that sound moves twice the distance 

Since speed moves at the same speed in the same media, moving through distance D would take = 2.6 s/2 = 1.3 s 

Distance = Speed * Time = 340 m/s * 1.3 s = 442 m 

4. 

Acceleration = change in velocity/ change in Time 

Acceleration = 22 m/s / 5 s = 4.4 m/ 

5. 

Acceleration =  / change in Time 

Acceleration = (21 m/s – 30 m/s)/ 3 s = - 3 m/ 

6. 

Acceleration = change in velocity/ change in Time 

Since the velocity remains constant, the change in velocity = 0 

Acceleration = (22 m/s – 22 m/s)/ 5 s = 0 m/ 

7. 

Velocity just before the stone touches down is the final velocity 

Gravitational acceleration = -9.8 m/  , assuming no air resistance 

Initial velocity, u is the velocity before release of the rock = 0 

Acceleration, a =   

From the equation v-u = at 

Final velocity, v = u + at 

Where t is the time taken to fall to the ground, t=2.5s 

Final velocity, v = 0 + (-9.8 m/  * 2.5 s) = - 24.5 m/s 

8. 

a) Velocity at maximum height is 0 m/s. 

b) The ball experience gravitational acceleration of -9.8 m/ 

c) Velocity at maximum height is final velocity, v 

Gravitational acceleration, a = -9.8 m/  , assuming no air resistance 

Initial velocity, u is the velocity with which the ball is thrown up from the ground level u = 19.6 m/s. Acceleration, a =   

Multiplying by t on both sides of the equation, we have v-u = at 

Final velocity, v = u + at 

Where t is the time taken to reach the maximum height. 

Substituting values into the equation we have 

0 m/s = 19.6 m/s + (-9.8 m/  * t) 

t = - 19.6 m/s /-9.8 m/  = 2 s 

d) Time taken from ground to maximum is equal to time taken from maximum to ground. 

Time taken from launching to maximum and back is therefore = 2* 2 s = 4 s 

9. 

Based on Newton’s Second Law of motion, Force is a product of Mass and acceleration 

Force (F) = Mass (M) Acceleration (a) 

The equation can also be written as  = M * a, meaning that the net force acting on an object equal to the product of mass and acceleration. This is because forces may act in different directions. 

Acceleration =  / change in Time 

Final velocity, v = 18 m/s 

Initial velocity, u = 10 m/s 

Time, t = 2 s 

Acceleration, a = 

Acceleration = (18 m/s – 10 m/s)/ 2 s = 4 m/ 

  = M * a 

Mass = 800 kg 

  = 800 Kg * 4 m/  = 3200 N 

10. 

Based on Newton’s Second Law of motion, Force is a product of Mass and acceleration 

  = M * a 

Acceleration =  / change in Time 

Final velocity, v = 0 m/s, because the car comes to a halt 

Initial velocity, u = 30 m/s 

Time, t = 5 s 

Acceleration, a = 

Acceleration = (0 m/s – 30 m/s)/ 5 s = -6 m/ 

  = M * a 

Mass = 1000 kg 

  = 1000 Kg * -6 m/  = - 6000 N 

Force is 6000 N acting opposite the direction that the car is moving. The force is equal to the force of acting on the moving car meaning that the car stops because the net force is zero. 

11. 

a) Gravitational acceleration = 9.8 m/s 2 , 

Weight of box is force due to gravitational acceleration 

Weight = F = Mass (m) × 9.8 m/s 2 

Mass = 1.5 kg 

F = 1.5 Kg × 9.8 m/s 2 = 14.7 N 

b) 

Force to the right = 12 N 

Force to the left = 15 N 

The net Force,  = 12 N – 15 N = 3 N to the left 

c) 

Based on Newton’s Second Law of motion, Force is a product of Mass and acceleration 

  = M * a 

a =  / m 

a = 3 N / 1.5 Kg = 2 m/  to the left.