A projectile is launched vertically from the ground at t=0 and its velocity in flight (in m/s) is given by v(t)=20-10t Find the position function, the displacement, and total distance traveled after t seconds for 0≤t≤4, assuming s(0)=0.

Question

A projectile is launched vertically from the ground at  t=0 and its velocity in flight (in m/s) is given by v(t)=20-10t  Find the position function, the displacement, and total distance traveled after t seconds for 0≤t≤4, assuming s(0)=0.

oobleck · Answer

v(t) = 20-10t s(t) = 20t-5t^2 the displacement is just s(t) Since the maximum height of 20 is reached at t=2, the distance traveled is s(t) for 0≤t≤2 40-s(t) for 2≤t≤4 since the total distance traveled will be 40 at t=4