Find Velocity using a limit

Question

Use the position function s(t)= -16t² + 98 to find the velocity in feet/seconds at time t= 1 second. The velocity at t=c seconds is given by lim t>c , s(c)-s(t)/c-t

 

please show all work

Answer 1

s(t)=-16t² + 98

lim_t-->c(s(c)-s(t))/(c-t). So, for c=1

 

lim_t-->1(s(1)-s(t))/(1-t)=lim_t-->1(82-98+16t²)/(1-t)=

=16limt-->1(t²-1)/(1-t)=-16lim_t-->1(t+1)=-32.

 

Answer 2

s(1 + h) = 16(1 + h)² + 98 = 16 + 32h + 16h² + 98

s(1) = 16 + 98

 

[s(1+h) - s(1)]/h = (32h + 16h²)/h  = 32 + 16h

 

lim (as h -> 0) [s(1+h)-s(1)]/h = instantaneous velocity at t = 1 = 32