Question

The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion

s = 4 sin(πt) + 2 cos(πt),

where t is measured in seconds. (Round your answers to two decimal places.)

Answer 1

Complete Question

The displacement (in centimetres) of a particle moving back and forth along a straight line is given by the equation of motion

s = 4 sin(πt) + 2 cos(πt),

where t is measured in seconds. (Round your answers to two decimal places.)

(a) Find the average velocity during each time period.

i. [1,2]

ii. [1 ,1.1]

iii. [1, 1.01]

Answer:

`V_A_1=4m/s`

`V_A_2=-11.38m/s`

`V_A_3=-12.47m/s`

Explanation:

From the question we are told that

Equation of motion is given by

`s = 4 sin(\pi t) + 2 cos(\pi t)`

Generally equation for average velocity is mathematically given by

`V_A=(S(y)-S(x))/(y-x)`

`V_A=(4 sin(\pi t) + 2 cos(\pi t)(y)-(4 sin(\pi t) + 2 cos(\pi t))(x))/(y-x)`

a) Co-ordinate(1,2)

`V_A=(4 sin(\pi y) + 2 cos(\pi y)-(4 sin(\pi x) + 2 cos(\pi x)))/(y-x)`

`V_A=(4 sin(\pi 2) + 2 cos(\pi 2)-(4 sin(\pi) + 2 cos(\pi)))/(2-1)`

`V_A=(0+ 2*1-(0 + 2)*-1)/(2-1)`

`V_A_1=4m/s`

b)Co-ordinate(1,1.1)

`V_A_2=(4 sin(\pi 1.1) + 2 cos(\pi 1.1)-( sin(\pi ) + 2 cos(\pi )))/(1.1-1)`

`V_A_2=(0+ 2*-1-(-0.30902*2)+2*-0.95106)/(1.1-1)`

`V_A_2=(((-0.30902*2)+2*-0.95106)-(0+ 2*-1))/(1.1-1)`

`V_A_2=(((-3.1382)-(-2))/(1.1-1)`

`V_A_2=-11.38m/s`

c) Co-ordinate(1,1.01)

`V_A_3=(4 sin(\pi 1.01) + 2 cos(\pi 1.01)-( sin(\pi ) + 2 cos(\pi))/(1.01-1)`

`V_A_3=(0.2214045768+1.996933901)-(-2))/(1.01-1)`

`V_A_3=((-2.12)-(-2))/(1.01-1)`

`V_A_3=-12.47m/s`