Answer
v= 165 ft/s
$a= 48ft/s^{2}$
$s_t= 450 ft$
$v_avg= 25 ft/s$
$(v_sp)v_avg=45 ft/s$
Work Step by Step
$s=t^3-6t^2-15t+7$
$v=\frac{ds}{dt}=3t^2-12t-15$
Substituting t when t is 10s
v= 165ft/s
$a=\frac{dv}{dt}=6t-12$
therefore when t is 10s
$\:a=\frac{48ft}{^{s^2}}$
If v = 0
$0=3t^2-12t-15$
Evaluating the equation above, we get its positive root to be
t = 5s
Therefore:
If t = 0. s = 7ft
If t=5s, s = -93 ft
If t = 10s, s= 257ft
The total distance will be:
$s_t = 7+ 93+93+257 = 450 ft$
instantaneous velocity velocity
$(v_sp)v_avg=\frac{ds}{dt}=\frac{257-7}{10-0}= 25ft/s$
Instantaneous acceleration
$(v_sp)_avg=$\frac{s_t}{dt}=\frac{450}{10}=45 ft/s$