Answer to Question #334228 in Calculus for Nzuzi

Question

Q.4) If an object starts out at rest and falls a distance of s feet in t seconds, then physical laws imply that s = 16t². Find ∆s/∆t as t changes from t0 to t0 + ∆t.

Use the result to find ∆s/∆t as t changes from:

(a) 3 to 3.5, (b) 3 to 3.2, and (c) 3 to 3.1

Answer 1

$$\Delta s=s(t_0+\Delta t)-s(t_0)$$

$$=16(t_0+\Delta t)^2-16(t_0)^2$$

$$=32t_0\Delta t+16(\Delta t)^2$$

$$\Delta s/\Delta t=32t_0+16\Delta t$$

(a) $t_0=3 , \Delta t=3.5-3=0.5$

$$\Delta s/\Delta t=32(3)+16(0.5)=104$$

(b) $t_0=3 , \Delta t=3.2-3=0.2$

$$\Delta s/\Delta t=32(3)+16(0.2)=99.2$$

(c) $t_0=3 , \Delta t=3.1-3=0.1$

$$\Delta s/\Delta t=32(3)+16(0.1)=97.6$$