Conceptual
Derivatives
Integrals
Kinematics
Vectors
100
what is the difference between average and instantaneous velocity.
instantaneous= velocity at the moment in time. average= average velocity over an amount of time.
100
What is the derivative of a position vs time graph.
the instantaneous velocity.
100
How do you integrate an equation with addition in it?
You integrate each section and then add them together. (more explanation will be given)
100
What are the three equations used when solving a kinematics problem.
1) Vf^2=Vo^2+2(a)(delta x) 2) Vf=Vo+a(t) 3) (delta x)= Vo(t)+(1/2)(a)(t)^2
100
What is the method to change a vector into its component form.
To use Trigonometry to separate the vector into its i and j components.
200
A graph of the motion of an object is plotted with the velocity on the vertical axis and the time on the horizontal axis. Which of these quantities CANNOT be determined from this graph? 1. the displacement from time t = 0 2. the initial velocity at t = 0 3. the acceleration of the object 4. the average velocity of the object 5. All four of the quantities can be determined from the graph.
5. All four of the quantities can be determined from the graph.
200
What is the derivative of sin(t) and e^(t)
cos(t) and e^(t)
200
when given an acceleration vs time function, what are the two methods of finding the velocity. (average and/or instantaneous)
1) graph and count the area under the curve. 2) take the integral of the function (if possible)
200
a ball is thrown at 35 (degrees) above the horizon at 90mph what is the i and j components of this throw. (in the +x direction)
i=73.7 mph j=51.6 mph
200
Add the components together (3i+5j) and (-4i+3j)
-i+8j
300
what does the derivative and integral of a velocity vs time graph give you?
derivative = acceleration integral = displacement
300
what is the derivative of t^n and ln(t)
n(t)^(n-1) and 1/t
300
What is the integral of sin(t) and cos(t)
Ssin(t)dt= -cos(t) Scos(t)dt= sin(t)
300
what are the two most important thing to do when solving a kinematics problem! (3 attempts)
Draw a picture that represents the given event. separate everything into its components
300
subtract the components and find the magnitude: (3i+5j) and (-4i+3j) 1st minus 2nd
(3i+5j) - (-4i+3j) = 7i+2j magnitude= 7.28 units
400
what is a unit vector?
it is a vector with a given direction and length of 1 unit
400
how do you take the derivative of f(g(t)) ie: sin(2t)
f'(g(t))*g'(t) ie: 2cos(2t)
400
What is the integral of t^n and e^t
S t^n dt = 1/(n+1) t^(n+1) S e^t dt = e^t
400
a penny is dropped from a roof top of 4m. What is the final velocity right before the penny hits the ground.
Vf^2 = 0^2 + 2 (-9.81m/s) (4m) answer: 8.85 m/s
400
A dog running through the neighborhood travels due west for 1.5 miles. It then heads north for 0.75 miles. Finally it heads southeast for 1 mile. What is the displacement of the dog?
1.68 mi
500
what is the acceleration felt by an object during free fall on earth. (and units)
Acceleration is due to gravity which is -9.81m/s^2
500
how do you take the derivative of d f(t) ___ ______ d(t) g(t)
g(t)f'(t)-f(t)g'(t) ______________ g(t)^2
500
a(t)= t^2+1/t+5 what is the velocity as a function of time? what is it at 2 seconds? (remember units!!)
v(t)= 1/3*(t)^3+ln(t)+5t = 1/3* 2^3+ln(2)+5(2) = 8/3+ln(2)+10 = 38/3+ln(2) = 13.36 m/s
500
during an experiment a particle needs to be accelerated at 2^6m/s^2 to a speed of .5c. (c= speed of light) If it starts from rest, how long, in seconds, would it take to get the particle up to speed. c= 3^8
s=150sec
500
A baseball comes off a bat with a speed of 80 mph at an angle of 35 degrees above the horizontal. What is the vertical component of the velocity? The horizontal component?
vertical=45.9 mph horizontal= 65.5 mph
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