To find the instantaneous velocity at t = 2 seconds, we need to integrate the given acceleration function to obtain the velocity function, and then evaluate it at t = 2 seconds.
Given: Acceleration, a(t) = 2t + 1 m/s² Initial velocity, v(0) = 1 m/s
To find the velocity function, we integrate the acceleration function with respect to time:
v(t) = ∫[a(t) dt] v(t) = ∫[(2t + 1) dt] v(t) = t^2 + t + C
To determine the constant of integration (C), we can use the initial velocity condition: v(0) = 1 m/s. Substituting t = 0 and v(0) = 1 into the velocity function:
1 = (0)^2 + (0) + C 1 = C
So, the velocity function becomes:
v(t) = t^2 + t + 1
Now, to find the instantaneous velocity at t = 2 seconds, we substitute t = 2 into the velocity function:
v(2) = (2)^2 + (2) + 1 v(2) = 4 + 2 + 1 v(2) = 7 m/s
Therefore, the instantaneous velocity at t = 2 seconds is 7 m/s.