Fundamentals of Physics-I Assignment # 1 Topics: Measurement, Vectors, Equations of kinematics, and Motion in 1-dimension Guidelines for Submission: 1. This is an individual homework assignment. 2....

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Fundamentals of Physics-I Assignment # 1 Topics: Measurement, Vectors, Equations of kinematics, and Motion in 1-dimension Guidelines for Submission: 1. This is an individual homework assignment. 2. This assignment should be neatly handwritten or may be typewritten. 3. The completed assignments must be scanned and submitted online through SLATE. Only PDF files are accepted, other formats will be ignored and will not be marked. The due date for online submission is Sept 23, 2021 (Thursday) by 11:59 PM. 4. Late submission will attract a 10% deduction per day, to a maximum of 30%. Assignments submitted after 3 days late will be awarded a grade of 0. 5. You are required to show all the steps. 6. You must take care of significant digits and units. 7. Total marks: 25 marks Q1. Water is poured into a container that has a small leak. The mass m of the water is given as a function of time t by m = 5.00t0.8 − 3.00t + 20.00, with t ≥ 0, m in grams, and t in seconds. (a) At what time is the water mass greatest, and (b) what is that greatest mass? In kilograms per minute, what is the rate of mass change at (c) t = 2.00 s and (d) t = 5.00 s? (Hint: Differentiate mass with respect to time) (5 marks) Q2. The position of a particle moving along the x axis is given in centimeters by x = 9.75 + 1.50t3, where t is in seconds. Calculate (a) the average velocity during the time interval t = 2.00 s to t = 3.00 s; (b) the instantaneous velocity at t = 2.00 s; (c) the instantaneous velocity at t = 3.00 s; (d) the instantaneous velocity at t = 2.50 s; and (e) the instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s. Write your final answers in centimeters and seconds. (5 marks) Q3. (a) If the position of a particle is given by x = 20t − 5t3, where x is in meters and t is in seconds, when, if ever, is the particle’s velocity zero? (b) When is its acceleration a zero? (c) For what time range (positive or negative) is a negative? (d) Positive? (4 marks) Q4. (a) If the maximum acceleration that is tolerable for passengers in a subway train is 1.34 m/s2 and subway stations are located 806 m apart, what is the maximum speed a subway train can attain between stations? (b) What is the travel time between stations? (c) If a subway train stops for 20 s at each station, what is the maximum average speed of the train, from one start-up to the next? (4 marks) Q5. A rock is thrown vertically upward from ground level at time t = 0. At t = 1.5 s it passes the top of a tall tower, and 1.0 s later it reaches its maximum height. What is the height of the tower? (3 marks) Q6 In a meeting of mimes, mime 1 goes through a displacement ( ) ( )1 ˆ ˆ4.0 m i + 5.0 m jd = and mime 2 goes through a displacement ( ) ( )2 ˆ ˆ3.0 m i + 4.0 m jd = − . What are (a) 1 2d d , (b) 1 2d d , (c) ( )1 2 2d d d+  , and (d) the component of 1d along the direction of 2d ? (4 marks)
Answered Same DaySep 22, 2021

Answer To: Fundamentals of Physics-I Assignment # 1 Topics: Measurement, Vectors, Equations of kinematics, and...

Shomik answered on Sep 23 2021
124 Votes
Q1. Water is poured into a container that has a small leak. The mass m of the water is given as a function of time t by m = 5.00t0.8 − 3.00t + 20.00, with t ≥ 0, m in grams, and t in seconds. (a) At what time is the water mass greatest, and (b) what is that greatest mass? In kilograms per minute, what is the rate of mass change at (c) t = 2.00 s and (d) t = 5.00 s? (Hint: Differentiate mass with respect to time)
(a) The equation for mass, m, of the water as a function of time, t, is
m = 5.00t0.8 − 3.00t + 20.00, with t ≥ 0 …. (i) where m is given in grams, and t is given in seconds.
Differentiating with respect to time and equating the result to 0 we get
…. (ii)
From the equation above, we get the time at which we will have the maximum value.
Therefore, the time at which we will have maximum value is given by
…. (iii)
Differentiating equation (i) again we get …. (iv)
From equation (iii) the resulting value given, by using the value of t from equation (ii), is less than 0 which means that the value obtained for time, t, will give the maximum value for mass, m.
(b) Therefore the greatest mass will be given by
m = 5
(c) The rate of mass change in kilograms per minute is given by
.
Therefore, the rate of mass change at t = 2.00 s is
(d) Therefore, the rate of mass change at t = 5.00 s is
Q2. The position of a particle moving along the x axis is given in centimeters by x = 9.75 + 1.50t3, where t is in seconds.
Calculate
(a) the average velocity during the time interval t = 2.00 s to t = 3.00 s;
(b) the instantaneous velocity at t = 2.00 s;
(c) the instantaneous velocity at t = 3.00 s;
(d) the instantaneous velocity at t = 2.50 s; and
(e) the instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s. Write your final answers in centimeters and seconds.
(a) The...
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