Distance, Rate, and Time
Can the size of your tires save you gas?
Unit Conversions
1 m = 3.28 ft.
1 m = 1,000 mm
1 m = 100 cm
1 ft. = 12 in.
Constant Acceleration Equations: ?
v = v0 + axt
Δ x = 1/2(v0 +v)t
Δ x = v0t + (1/2) at2
v2 = (v0)2 +2a Δ x
Meaning of variables:
v = final velocity
v0 = initial velocity
a = acceleration
t = time
Δ x = change in distance or how far
Other Useful Equations:
Circumference of a circle = 2πr, where r = radius of circle and π = 3.14
Diameter of circle = 2r
Your Tires:
Wheels are 1.25 inches in diameter.
Fastest speed is 3 ft/second.
Maximum distance to travel is 16 x (18 cm).
1.?Convert the dimensions for the wheel and maximum distance to feet.
Wheel diameter in feet: _____________
Maximum distance in feet: ______________
A 5% error in distance is allowed. What is the total distance if the 5% error is applied?
Shorter distance with error: __________
Longer distance with error: __________
2.?How many times does the wheel turn to travel the maximum distance? ______
?If you take into account the 5% error, how does this affect the number of turns of the wheel?
3.?How long does it take to travel the maximum distance at full speed? _______
?Is this impacted by the distance error? How?
4.?What is the acceleration needed to travel the maximum distance when starting from a standstill?
How is acceleration impacted by the distance error?
5.?Examine the pathways below. Calculate the time to travel each path, taking into account slowing and turning time. Also calculate the number of turns of the wheel on each path segment. The star is the finish. Corridors are 16.2 cm wide. Be specific about the time you allow for slowing and turning.
9.5 ft.
9.5 ft.
?
3 ft.
2.5 ft.
???Start
??Assume all blocked areas are 16.2 cm wide unless specified.
?Assume all corridors are 16.2 cm wide, except for the one containing the star.
Which path is the fastest? Shortest? Why? (Do you have to slow more on a sharp turn?)
Could you use the number of wheel turns to determine the path of motion?