Answer:
the maximum velocity of the mass v (max) = 2 ft/s
the amount of time it takes for the mass to move from its lowest position to its highest position∆t = 1/3 seconds = 0.33 seconds
Explanation:
Given the velocity equation;
v=−2 cos(3πt)
The maximum velocity would be at cos(3πt) = 1 or cos(3πt) = -1
v (max) = -2 × -1 = 2 ft/s
The time taken for the mass to move from lowest position to highest position
At Lowest position, vertical velocity equals zero.
At highest position, vertical velocity equals zero.
The time taken for the mass to move from one v = 0 to the next v = 0
Cos(π/2) = 0 and
Cos(3π/2) = 0
For the first;
Cos(3πt) = cos(π/2)
3πt1 = π/2
t1 = π/2(3π)
t1 = 1/6 second
For the second;
Cos(3πt) = cos(3π/2)
3πt2 = 3π/2
t2 = 3π/2(3π)
t2 = 1/2 second
∆t = t2 - t1 = 1/2 - 1/6 = 3/6 - 1/6 = 2/6 = 1/3 seconds
∆t = 1/3 seconds
