Question

1a. Three digital clocks A, B, and C run at different rates and do not have simultaneous readings of zero. The figure shows simultaneous readings on pairs of the clocks for four occasions. (At the earliest occasion, for example, B reads 25.0 s and C reads 92.0 s.) If two events are 700 s apart on clock A, how far apart are they on (a) clock B and (b) clock C? (c) When clock A reads 390 s, what does clock B read? (d) When clock C reads 14 s, what does clock B read? (Assume negative readings for prezero times.)

1b.

Water is poured into a container that has a leak. The mass m of the water is given as a function of time t by m = 4.8t^0.8 - 3.2t + 17, 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? What is the rate of mass change at (c) t = 1.8 s and (d) t = 5.4 s?

1c.Water is poured into a container that has a leak. The mass m of the water is given as a function of time t by , with t ≥ 0, m in grams, t in seconds, and A, B, and C positive constants. In terms of A, B, C and t, (a) find a formula for the rate of mass change as a function of t. (b) At what time is the water mass greatest, and (c) what is that greatest mass?

1d.

A vertical container with base area of length L and width W is being filled with identical pieces of candy, each with a volume of v and a mass m. Assume that the volume of the empty spaces between the candies is negligible. If the height of the candies in the container increases at a certain rate per unit time dH/dt, at what rate per unit time does the mass of the candies in the container increase?

Answer 1

In the ques 1a and 1c complete information is not given so I will only solve 1b and 1d

1b).

i. differentiate above

ii greatest mass

iii rate of mass change

1d)

volume,

Number of candies/sec

                                      

rate of mass increase