1. ht= -4.9t2+ 450, where t is the time elapsed in seconds and h is the height in metres.
a) Table of Values
t(s) | h(t) (m) | 0 | ht= -4.9(0)2+ 450= 450 | 1 | ht= -4.9(1)2+ 450= 445.1 | 2 | ht= -4.9(2)2+ 450= 430.4 | 3 | ht= -4.9(3)2+ 450= 405.9 | 4 | ht= -4.9(4)2+ 450=371.6 | 5 | ht= -4.9(5)2+ 450=327.5 | 6 | ht= -4.9(6)2+ 450= 273.6 | 7 | ht= -4.9(7)2+ 450= 209.9 | 8 | ht= -4.9(8)2+ 450= 136.4 | 9 | ht= -4.9(9)2+ 450=53.1 | 10 | ht= -4.9(10)2+ 450= -40 |
b) Average velocity for the first 2 seconds after the ball was dropped=
h2-h02-0 = 430.4-4502-0 = -19.62 = -9.8 m/s
c) Average velocity for the following time intervals:
i. 1≤t≤4 = h4-h14-1 = 371.6-445.14-1 = -73.53 = -24.5 m/s
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Substitute these values into the equation and simplify to find the instantaneous rate of change of a function.
b) Evaluate the following limits:
i. limx→0x-32x2-5 = 0-3202-5 = -3-5 = 35 = 0.6
ii. limx→22x2-7x+6x-2 = 222-72+62-2 = 00
Therefore, limx→22x2-7x+6x-2 = 2x-3x-2x-2 = limx→22x-3= 1
5. ht= -5t2+ 20t+1, where h is height in metres and t is the time in seconds.
a) h2=-522+ 202+1 = 21
h2+h= -52+h2+ 202+h+ 1 = -54+4h+h2+ 202+h+ 1 = -54+4h+h2+40+20h+1 = -20-20h-5h2+40+20h+1 = -5h2+21
Instantaneous velocity of the ball at t= 2 seconds is
lim h→0h2+h-h2h = -5h2+21-21h = -5h2h = h-5hh = -5h limh→0-5h= -50=0
Therefore the instantaneous velocity of the ball at t= 2 seconds is 0 m/s.
QUESTION 5 CONTINUED
b) dt= t2-8t+15, where d is measured in metres and t is the time in seconds.
The particles is at rest when t= 4 seconds and therefore the instantaneous velocity of the particle at t= 4 seconds should be 0 m/s.
d4=42- 84+15= -1 d4+h=4+h2-84+h+ 15 = 16+8h+h2-84+h+15 = 16+8h+h2-32-8h+15 = h2+16-32+15 = h2-1 Instantaneous velocity of the particle at t= 4 seconds is lim h→0d4+h-d4h = h2-1+1h = h2h = hhh = h limh→0h= 0
Therefore the instantaneous velocity of the particle at t= 4 seconds is 0 m/s and hence
c. How many yards are equivalent to 2,500 meters? Round your answer to the nearest hundredth, if necessary.
The purpose of this lab was to test the relationship between velocity, position and time. As well as identify how accelerations affects an object's velocity and time. In this experiment, we will collect data on velocity, speed, and time. We used the equation Y=mx+b, in order to compare the velocity of each trial by comparing the slope and the y-intercept. If the slope was steeper on the graph, this meant that the cart had an increase in velocity. If the cart maintains at a constant speed, then the cart will have an increase in acceleration. In class we learned about the principles of acceleration, time, and velocity. Acceleration is an object’s increase in velocity. Velocity is how
b. The width of a normal sheet of paper is 8.5 inches. Convert this length to kilometers. (4 points)
Draw a graph that shows the distance Jacob’s car is from his house with respect to time. Remember
SQRT(2 * F * T / H) = (2 * 80 * 200,000 / 1.00)0.5
1. During gym class, four students decided to see if they could beat the norm of 45 sit‐ups in a minute. The first student did 64 sit‐ups, the second did 69, the third did 65, and the fourth did 67.
The propagation delay = 2d x (20ms/km) = (2x10) x (20ms/km) = 0.4 seconds or 400 ms.
3) What do the rate of change values you just calculated represent? Why are some positive and some negative?
T= 40ms, I figured this by guessing cause I could not find any information on how to calculate. So I used the equation for t and plugged in different numbers until I got the 10ms that was already given in the table. t= T x 0/360= 40ms x 90/360= 0.01 x 10^-3= 10ms
9) Since you are plotting displacement on the y-axis and time on the x-axis, this is an example
The function in Figure 1 can be expressed as a simple equation: D 500 h 500 50 h ,
Step 9: Because we measured the lengths in centimeters rather than meters, we need to calculate are ‘g’ value into m/s2 so we can compare it to the SI unit for acceleration due to gravity. (Eg. 981.4/100 = 9.81 m/s2)
Will be used with C equal to the height of the center of gravity of the vaulter in meters.
Materials: meter stick stopwatch bathroom scale (optional) 1. Devise a plan to make the measurements and calculate the work you must do to climb a flight of stairs as well as the rate at which you do it (your power). Use standard metric units. After your teacher approves your plan, carry it out under your teacher’s direction.