1) An American football player, starting from rest at the line of scrimmage, accelerates along a straight line for a time of 1.25 s. Then, during a negligible amount of time, he changes the magnitude of his acceleration to a value of 1.2 ms-2. With this acceleration, he continues in the same direction for another 1.2 s, until he reaches a speed of 3.7 m s-1. What is the value of his acceleration (assumed to be constant) during the initial 1.25 s period?
i. Sketch a plot of velocity versus time.
ii. To solve this problem, you have to work backwards. If the final speed is 3.7 m s-1 after accelerating at 1.2 m s-2 for 1.2 s, then what velocity did he have before this 1.2 s burst of acceleration?
iii. It took the player 1.25 s to reach this velocity, accelerating from rest. What was the initial acceleration?
2) Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 1 hour, reaching a point 2 km farther upstream. At this point they realize that the bottle is missing and, driven by ecological awareness, they turn around and head downstream. They catch up with and retrieve the bottle (which has been moving along with the current) 5 km downstream from the turn-around point. Assuming a constant paddling effort throughout, how fast is the river flowing? What would the canoe speed in a still lake be for the same paddling effort?
The unknown variables in this problem seem to be the speed of the river, the speed of the canoe relative to the river and the time it takes from when they turn around to when they retrieve the bottle. 3 unknowns.
i. Write down an equation in terms of the 3 unknowns for the students canoeing upstream. This is of the form, velocity is equal to distance over time.
ii. Write down a similar equation in terms of the 3 unknowns for the students canoeing down stream to retrieve the bottle.
iii. Write down a similar equation in terms of the 3 unknowns for the journey of the bottle from when it was first dropped to when it was retrieved.
iv. You now have 3 equations and 3 unknowns. Do the algebra and solve the problem.
3) The mass of an ant is 5.5x10-6 kg. What is this in grams (g), milligrams (mg) and micrograms ( g)?
A dose of a given antibiotic for an infant is one micro-liter per hour (1 μl h-1 ). What is this in meters μcubed per second (m3s-1 ) and liters per year (l year-1)?
2.6cm 1/100 cm = 0.026m
To change units simply multiply by a conversion factor. For example, to convert 2.6 cm to m would be where the fraction is the conversion. Note 100 cm is equivalent to 1 m, so multiplying the 2.6 cm by this fraction doesn't change the quantity just the units.