Physics with Calculus
For one-dimensional motion, what does the position function x(t)x(t) represent?
An object's position is x(t)=3t2−2t+1x(t) = 3t^2 - 2t + 1 meters. What is its average velocity from t=1t = 1 s\(\text{s}\) to t=3t = 3 s\(\text{s}\)?
If x(t)=5t3−4t+2x(t) = 5t^3 - 4t + 2 meters, what is the instantaneous velocity at t=2t = 2 s\(\text{s}\)?
An object moves with velocity v(t)=4t+1v(t) = 4t + 1 m/s\(\text{m/s}\). What is its displacement from t=0t = 0 s\(\text{s}\) to t=3t = 3 s\(\text{s}\)?
A particle has velocity v(t)=8t−3v(t) = 8t - 3 m/s\(\text{m/s}\) and satisfies x(2)=11x(2) = 11 m\(\text{m}\). What is its position function?
