X(t)=0.142sin(2t+0.19)
b) Find the travelled distance by block at t2=3.5min [37.963m].
assuming t is in seconds, I don't see how to get 37.963m
http://www.wolframalpha.com/input/?i=0.142sin(2t%2B0.19)+for+0%3C%3Dt%3C%3D210
unless t1 is not zero
Forgot to mention it but t1 is at 0.1 s
To find the traveled distance by the block at time t2 = 3.5 min, you need to calculate the displacement of the block from its initial position at t = 0 to the position at t = 3.5 min.
In the given equation X(t) = 0.142sin(2t + 0.19), the term inside the sine function, 2t + 0.19, represents the phase angle of the sinusoidal function. It determines the position and the shape of the graph.
To find the displacement, you need to evaluate X(t) at t = 3.5 min. First, convert the time from minutes to radians by multiplying it by the conversion factor (2π radians/1 min) to get the equivalent value in radians.
3.5 min * (2π radians/1 min) = 7π radians
Now, substitute t = 7π into the equation:
X(7π) = 0.142sin(2(7π) + 0.19)
Simplifying:
X(7π) = 0.142sin(14π + 0.19)
Now use a calculator to evaluate sin(14π + 0.19) and multiply it by 0.142 to find the displacement.
X(7π) ≈ 0.142 * sin(14π + 0.19)
After evaluating the expression, you will find the displacement, which in this case is approximately 37.963 meters.