1. Vectors and Calculus

2. Position, Velocity, Acceleration
The position of a particle on a number line is given by the equation p(t) = 𝑡 2 −5𝑡+6 for 𝑡≥0.
Find a velocity equation for the particle.
Find an acceleration equation for the particle.
What is the speed of the particle at time 𝑡=2?
Is the particle speeding up or slowing down at this point?
At what time does the particle stop?

3. Position, Velocity, Acceleration
A particle moves in a PLANE according to the parametric curve 𝑥 𝑡 =2𝑡−1, 𝑦 𝑡 =2 𝑡 2 −5𝑡+1, where t is time in seconds.
Find a position vector for the particle.
Find a velocity vector for the particle.
Find an acceleration vector for the particle.
At what time, if any, does the particle stop?
What is the speed of the particle at time 𝑡=5?
How far has the particle traveled after 5 seconds?

4. Acceleration, Velocity, Position
An object is dropped from a building (initial velocity is 0) that is 10 meters high (initial position is 10).
Write an acceleration equation (Remember that acceleration due to gravity is approximately -9.8 m/sec2.
Write a velocity equation.
Write a position equation.
At what time does the object hit the ground?

5. Acceleration, Velocity, Position
The acceleration vector for a particle moving in a PLANE is 3𝑡, cos 𝑡 , where t is time in seconds. At 𝑡=0, the particle has velocity 5, 1 and is at position (1, −1).
Find the velocity vector.
Find the position vector.
What is the speed of the particle at time 𝑡=3?
Is the particle ever at the origin? If so, at what time does this occur?

6. A.P. BC Test Calculator
For 0≤𝑡≤3, and object moving along a curve in the xy-plane has position 𝑥 𝑡 , 𝑦(𝑡) with 𝑑𝑥 𝑑𝑡 = sin 𝑡 3 and 𝑑𝑦 𝑑𝑡 =3 cos 𝑡 At time 𝑡=2, the object is at position (4, 5).
Write an equation for the line tangent to the curve at (4, 5).
Find the speed of the object at time 𝑡=2.
Find the total distance traveled by the object over the time interval 0≤𝑡≤1.
Find the position of the object at time 𝑡=3.