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.)
(a) Find the average velocity during each time period.
(i) [1, 2]
To find the average velocity during the time period [1, 2], we need to calculate the displacement of the particle at times 1 and 2, and then divide by the time interval.
The displacement of the particle at time t is given by the equation of motion s = 4 sin(πt) + 2 cos(πt).
At time t = 1, the displacement is:
s(1) = 4 sin(π*1) + 2 cos(π*1) = 4 sin(π) + 2 cos(π) = 4(0) + 2(-1) = -2 cm
At time t = 2, the displacement is:
s(2) = 4 sin(π*2) + 2 cos(π*2) = 4 sin(2π) + 2 cos(2π) = 4(0) + 2(1) = 2 cm
The time interval is 2 - 1 = 1 second.
Now, we can calculate the average velocity as the displacement divided by the time interval:
Average velocity = (displacement)/(time interval)
Average velocity = (-2 cm - 2 cm)/1 second = -4 cm/second
Therefore, the average velocity during the time period [1, 2] is -4 centimeters per second.
avg velocity over [1,2] is just
[(f(2)-f(1)]/(2-1)
Now just plug and chug