A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 4. f(t) = 12t² + 35 t + 1
Answer:
Velocity = 131 m/s
Speed = 131 m/s
Explanation:
Equation of motion, s = f(t) = 12t² + 35 t + 1
To get velocity of the particle, let us find the first derivative of s
v (t) = ds/dt = 24t + 35
At t = 4
v(4) = 24(4) + 35
v(4) = 131 m/s
Speed is the magnitude of velocity. Since the velocity is already positive, speed is also 131 m/s
Answer:
a) 0.658 seconds
b) 0.96 inches
Explanation:

Time taken by the ball to reach the highest point is 0.14 seconds

The highest point reached by the snowball above its release point is 0.315 ft
Total height the snowball will fall is 4+0.315 = 4.315 ft

The snowball will reach the bank at 0.14+0.518 = 0.658 seconds after it has been thrown


The snowball goes 0.5-0.42 = 0.08 ft = 0.96 inches
When the same masses are heated by the same amount copper will heat up the fastest. Copper is a good conductor of heat that is why it easily heats up. Gold is not a good conductor of heat because of its stable properties.
This question involves the concepts of equilibrium and Newton's third law of motion.
The support force will be "1 pound" for the empty bucket and the support force will be "6 pounds" after pouring water into it.
- According to the condition of equilibrium, the sum of forces acting on a stationary object must be zero. Hence, the support force of the table will be equal to the total mass of the bucket.
- According to Newton's Third Law of Motion every action force has an equal but opposite reaction force. Hence, the support force will be a reaction force to the weight of the bucket.
Therefore, the support force in each case will be equal to the total mass of the bucket:
Case 1 (empty bucket):
<u>support force = 1 pound</u>
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Case 1 (water poured):
support force = 1 pound + 5 pound
<u>support force = 6 pound</u>
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Learn more about equilibrium here:
brainly.com/question/9076091