Question

Given: A particle is moving along a straight line such that its velocity is defined as v = (-4s2) m/s, where s is

in meters.

Find: The velocity and acceleration as functions of time if s = 2 m when t = 0.

Answer 1

$V= \frac {ds}{dt}$

$V=-4s^2 m/s$

$\frac {ds}{dt}=-4s^2$

$S= \frac {1}{4t+ \frac{1}{2}}$ $=\frac {2} {8t+1}m$

$v=\frac{ds}{dt}= \frac {d}{dt}$ $=(\frac {2}{8t+1})$ $=$ $=\frac {-16}{(8t+1)^2}$

$velocity= \frac {-16}{(8t+1)^2}$

$a=\frac{dv}{dt}$ = $\frac{16(2)(8t+1)(8)}{(8t+1)^4}$

$a= \frac {256}{(8t+1)^3} m/s^2$