Question

particle with velocity v(t) = t^2 +3, where r is time in seconds, moves in a straight line. How far does the particle move from t=2 to t= 3 seconds?

Answer 1

Integrate the velocity function over [2, 3]:

`\displaystyle \int_2^3 (t^2+3) \, dt = \left(\frac{t^3}3+3t\right)\bigg|_2^3 = \boxed{\frac{28}3}`