#### Transcript of Math Project Partial 1

Understanding the problem

4. A rock is thrown upward and its position function at any time is given by

S(t)=-16t^2+64t+96

**Procedure**

b. Graph the position function, showing at least 3 points where the rock is passing through.

S(t)=-16t^2+64t+96

Amanda López A01226974

Cecilia Padilla A01226851

Ángela García A01225986

a. Calculate the derivative of the position function using the limit definition

b. Graph the position function, showing at least 3 points where the rock is passing through

c. Given the velocity function v(t)=-32t+64. Graph this function, using at least 2 points

d. Given the acceleration function a(t)=-32. Graph this function, using at least 2 points

e. What is the connection between position – velocity – acceleration?

f. Calculate the time when the velocity is the half of the initial velocity

a. Calculate the derivative of the position function using the limit definition

f. Calculate the time when the velocity is the half of the initial velocity

**Math Project Partial 1**

c. Given the velocity function

v(t)=-32t+64.

Graph this function, using at least 2 points.

d. Given the acceleration function

a(t)=-32

. Graph this function, using at least 2 points

e. What is the connection between position – velocity – acceleration?

X Y

1 32

2 0

3 -32

4 -64

y = m x + b

V(t)=-32t+64

V(t)=-32(0)+64=64

V(t)=-32(1)+64=32

V(t)=-32(2)+64=0

V(t)=-32(3)+64=-32

V(t)= -32(4)+64=-64

(1,-32)

(2,-32)

s(0)=-16(0)^2+64(0)+96= 96

2(1)=-16(1)^2+64(1)+96= 144

s(2)=-16(2)^2+64(2)+96= 160

s(3)=-16(3)^2+64(3)+96= 144

s(4)=-16(4)^2+64(3)+96= 32

X Y

0 96

1 144

2 160

3 144

4 32

The formulas of the position, velocity and acceleration are very closely related because they are derivatives of one another.

If you derivate the formula for the position, you will obtain the velocity. If you derivate the formula for the velocity, you will obtain the acceleration.

S''(t)= a(t), S'(t)= v(t)

(1,32)

(0,64)

(0,96)

(1,144)

(2,160)

Flowchart

Full transcript