AP Calculus



AP Calculus

Review #2 Notes

Position: s(t) or x(t), aka location

Displacement: How far you are from where you started.

s(1) = 6 and s(4) = 10, displacement is 4.

We discussed the sign of displacement. For right now, we’ll say it can be either neg. or pos.

Velocity: v(t)

Can be either negative or positive.

It is the first derivative of position.

When at rest, velocity is 0.

Moving left of down, velocity is negative. Right or up, velocity is positive.

Acceleration: a(t)

It is the second derivative of position.

It measures how velocity is changing.

Speed is the absolute value of velocity. It is NEVER negative.

When velocity and acceleration have same signs, object is speeding up. If different, slowing down.

To find derivative on calculator, when they are allowed:

If [pic]

MATH, 8

nDeriv(sin(X)cos(4X), X, [pic]

AP Calculus

Review #2 Notes

Position: s(t) or x(t), aka location

Displacement: How far you are from where you started.

s(1) = 6 and s(4) = 10, displacement is 4.

We discussed the sign of displacement. For right now, we’ll say it can be either neg. or pos.

Velocity: v(t)

Can be either negative or positive.

It is the first derivative of position.

When at rest, velocity is 0.

Moving left of down, velocity is negative. Right or up, velocity is positive.

Acceleration: a(t)

It is the second derivative of position.

It measures how velocity is changing.

Speed is the absolute value of velocity. It is NEVER negative.

When velocity and acceleration have same signs, object is speeding up. If different, slowing down.

To find derivative on calculator, when they are allowed:

If [pic]

MATH, 8

nDeriv(sin(X)cos(4X), X, [pic]

AP Calculus

Review #2

Calculators allowed

1. The position of a particle moving on the line y = 2 is given by [pic] where t is time in seconds.

a) Describe the motion (moving left or right) of the particle for t > 0.

b) When does the particle speed up?

c) When does the particle slow down?

d) When does the particle change direction?

e) When is the particle at rest?

2. The graph shows the velocity [pic]of a body moving along a coordinate line.

a) When does the body reverse direction?

b) When is the body moving at a constant speed?

c) Graph the body’s speed for [pic].

d) Graph the acceleration.

3. A particle P moves on the number. Its position as a function of time is shown below.

a) When is P moving to the left?

b) When is P moving to the right?

c) When is P standing still?

d) Graph the particle’s velocity and speed.

4. The graph shows the velocity of a particle moving on a coordinate line.

a) When does the particle move forward?

b) When does the particle move backward?

c) When does the particle speed up?

d) When does the particle slow down?

e) When is the particle’s acceleration positive?

f) When is the particle’s acceleration negative?

g) When is the particle’s acceleration zero?

h) When does the particle move at its greatest speed?

i) When does the particle stand still for more than an instant?

5. A particle moves along a line so that its position at any time t > 0 is given by the function [pic], where s is measured in meters and t is measured in seconds.

a) Find the displacement during the first 5 seconds.

b) Find the average velocity during the first 5 seconds.

c) Find the instantaneous velocity when t = 4.

d) Find the acceleration of the particle when t = 4.

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