Answer
a) $∆s$ = 11.025 m
b) $\frac{∆s}{∆t}$ = 22.05 m/s
c) The instantaneous velocity at t = 2 is 19.6 m
Work Step by Step
a)
$∆s$ = $s(2.5)-s(2)$
$∆s$ = $4.9(2.5)^{2}-4.9(2)^{2}$
$∆s$ = $30.625 - 19.6$
$∆s$ = $11.025$ m
b)
$\frac{∆s}{∆t}$ = $\frac{s(2.5)-s(2)}{2.5-2}$
$\frac{∆s}{∆t}$ = $\frac{11.025}{0.5}$
$\frac{∆s}{∆t}$ = 22.05 m/s
c)
time interval [2,2.01]
$\frac{∆s}{∆t}$ = $\frac{s(2.01)-s(2)}{2.01-2}$ = 19.649
time interval [2,2.005]
$\frac{∆s}{∆t}$ = $\frac{s(2.005)-s(2)}{2.005-2}$ = 19.6245
time interval [2,2.001]
$\frac{∆s}{∆t}$ = $\frac{s(2.001)-s(2)}{2.001-2}$ = 19.6049
time interval [2,2.00001]
$\frac{∆s}{∆t}$ = $\frac{s(2.00001)-s(2)}{2.00001-2}$ = 19.600049
The instantaneous velocity at t = 2 is 19.6 m
