1. Show that the particle whose displacement time equation is S=t3+12 moves from the origin always with a positive acceleration.
2. In a group of 1000 computers linked to each other via the internet, the number N infected with a virus at time t years is give by:
1000
N=-------------
1+Ce-1000t
where C is a constant. Suppose that when t=0 only one computer was infected with the virus. After how many days will 50% of the computers be infected?
3. An antibiotic is developed to kill a selected type of bacterium. In laboratory experiments, the number of bacteria, N and the time t, measured in minutes, are observed to fit the law:
dN
----= -5x10-3
dt
A bacterial count of 200,000 is potentially lethal unless it can be reduced to 100,000 within 3 hours. Is this antibiotic going to be effective? Explain your answer.
4. A pulley is located 25m above a crate which is on the ground at a point O. A 50m rope is passed over the pulley. One end is fastened to the crate and a machine moves the other end along the ground at a constant rate of 4m/s. At any time, let y be the height of the crate from O, and let the distances from the rope end on the machine to O and the pulley be x and d, respectively. How fast is the crate rising when it is 10m above the ground.
THANK YOU.
2. In a group of 1000 computers linked to each other via the internet, the number N infected with a virus at time t years is give by:
1000
N=-------------
1+Ce-1000t
where C is a constant. Suppose that when t=0 only one computer was infected with the virus. After how many days will 50% of the computers be infected?
3. An antibiotic is developed to kill a selected type of bacterium. In laboratory experiments, the number of bacteria, N and the time t, measured in minutes, are observed to fit the law:
dN
----= -5x10-3
dt
A bacterial count of 200,000 is potentially lethal unless it can be reduced to 100,000 within 3 hours. Is this antibiotic going to be effective? Explain your answer.
4. A pulley is located 25m above a crate which is on the ground at a point O. A 50m rope is passed over the pulley. One end is fastened to the crate and a machine moves the other end along the ground at a constant rate of 4m/s. At any time, let y be the height of the crate from O, and let the distances from the rope end on the machine to O and the pulley be x and d, respectively. How fast is the crate rising when it is 10m above the ground.
THANK YOU.