# AP calculus / Physics Question?

An object moves along the x-axis following the position function:

x(t) = - ( 3 / pi ) cos [ ( pi / 3 ) t ] + ( 3 / pi ) + 2

A) Are the statements both true, false or one true + one false? give your reasons

Statement 1: for 3 < t < 4.5, velocity is decreasing

Statement 2: for 3 < t < 4.5, the speed is increasing

I thought they were both true since velocity is becoming more negative:

t = 3, v = 0 then t = 3.5, v = -1m/s etc.

I think it is speeding up since the acceleration graph is all negative:

t = 3, a = -3m/s^2 then t = 4, a = -1 m/s^2

so am i right or am I wrong??

b) What is the total distance travelled in 4 s?

I thought you use the position function for intervals [0,3] since velocity is positive and [3,4] since velocity is negative...

so am i right???

please explain clearly

for part B), the object changes from positive velocity to negative velocity, so wouldn't that count as changing direction, so you use intervals 0,3 and 3,4???????

for part B), the object changes from positive velocity to negative velocity, so wouldn't that count as changing direction, so you use intervals 0,3 and 3,4???????

### 2 Answers

- Anonymous8 years agoBest Answer
Differentiate the function to get...

x'(t) = 3/π * π/3 * sin(πt/3)

= sin(πt/3)

Graph that function, and we have....

→Decreasing at 3 < t < 4.5

→Increasing at 3 < t < 4.5

Good luck!

Source(s): Σ - DandLv 58 years ago
x(t) = - ( 3 / pi ) cos [ ( pi / 3 ) t ] + ( 3 / pi ) + 2

v = dx/dt = (-3/pi) (pi/3) [-sin(t pi/3) = sin (pi/3) t

t = 3 ===> v = sin pi = 0

t = 4.5===> v = sin 3pi/2 = -1 ===> decreasing = statement 1

b)

x(4) = - ( 3 / pi ) cos [ ( pi / 3 ) 4 ] + ( 3 / pi ) + 2 = 1.5/pi + 3/pi + 2 =

= (4.5 + 2pi)/pi = 3.43