Position
How do you find the position given a velocity function?
Antiderive
how do you find velocity from position?
x'(t)
how do you find acceleration from position and from velocity
x''(t) and v'(t)
Find the velocity vector at t = 1 for an object traveling according to the parametric function x = t2 – 2t + 1, y = –t2 + 2.
v(1) = (0, -2)
j
j
f
f
If x=t^3 -t and y=(3t+1)^1/2 then dy/dx at t=1 is?
3/8
Find the average value of F(x)=3x^2-2x over the interval from x=1 to x=4
48
The velocity of the particle is traveling on a straight line given by the function v(t)=sin(t)+2^t
Find the total distance travelled by the particle from time t=0 to t=5
D= 45.439
If the position of an ant traveling along a horizontal path at time t is 2 3 1 t + , what is the ant’s average velocity from t = 1 to t = 6?
21
find a(t) if v(t)= 2t^2+4t+10
4t+4
h
h
k
k
b
d
d
g
g
A particle moves in the xy-plane with position vector x(t), y(t) such that x(t)=t^3-6t^2+9t+1 and y(t)=-t^2+6t+2 in the time interval 0 < t < 5.
Find the average speed of the particle for the time interval 0 < t < 5.
=6.609
A particle with velocity at any time t given by v(t)=e^t moves in a straight line. How far does the particle move from t=0 to t=2
e^2 -1
if Teddy's acceleration is given by a(t)=-32 and v(0)=10, what is the position function?
-16t^2+10t
e
e
A particle moves along the x‐axis so that its velocity at any time t > 0 is given by v(t)=tlnt-t. At time t = 1, the position of the particle is x(1)=6.
Write an expression for the acceleration of the particle
a(t)=lnt
i
i
l
l