To find the displacement of the object from t = 1 second to t = 4 seconds, we need to calculate the definite integral of the velocity function over that time interval. The integral of the velocity function will give us the change in position or displacement of the object.
Given the velocity function v(t) = -2t + 4, we can integrate it with respect to time (t) to find the displacement function.
∫v(t) dt = ∫(-2t + 4) dt
To integrate -2t + 4, we apply the power rule of integration:
∫(-2t + 4) dt = -t^2 + 4t + C
Now we can calculate the displacement from t = 1 second to t = 4 seconds by subtracting the value of the displacement function at t = 1 from the value of the displacement function at t = 4:
Displacement = [-(4)^2 + 4(4) + C] - [-(1)^2 + 4(1) + C] = [-16 + 16 + C] - [-1 + 4 + C] = 0 + C - (-1 + 4 + C) = 0 + C + 1 - 4 - C = 1 - 4 = -3 meters
Therefore, the displacement of the object from t = 1 second to t = 4 seconds is -3 meters.