Answer :
Final answer:
Displacement is obtained by integrating the acceleration function to get velocity and then integrating velocity to get displacement. Evaluate the displacement function at t = 0.764 to find the particle's displacement in the positive direction.
Explanation:
To find the displacement in the positive direction from t = 0 to t = 0.764, given that a particle has acceleration a = 39.3 t3 e-2t and at time t = 0 velocity is zero, we first need to integrate the acceleration function to find the velocity function since velocity is the integral of acceleration. Then, we integrate the velocity function to find the displacement since displacement is the integral of velocity.
The velocity v(t) as a function of time t would be:
v(t) = ∫ a(t) dt = ∫ 39.3 t3 e-2t dt
After finding the velocity function, we would perform another integration to obtain the displacement:
s(t) = ∫ v(t) dt
We would then evaluate the displacement function at t = 0.764 to find the displacement during the given time interval.
