Name:

'roblem $2$:

$4+5+3=12$ Points

$t$ boat as shown in Figure $2,$ travels along the stream with an initial horizontal velocity of $6\frac{m}{s}.$

its horizontal acceleration varies linearly from $-12\frac{m}{s^2}$ at $t=0$ to $-2\frac{m}{s^2}$ at $t=t_1$ and then

remains equal to $-2\frac{m}{s^2}$ until $t=1\mathrm{.}4s.$ Given that $v=1\mathrm{.}8\frac{m}{s}$ when $t=t_1.$

$($a$)$ Draw acceleration$-$time & velocity$-$time curves with the given data $(2+2=4$ Points$)$

$($b$)$ Determine time $t_1,(5$ Points$)$

Note: $($figures need not be to scale$)$

$($c$)$ Determine velocity of the boat $v_{1\mathrm{.}4}$ at $t=1\mathrm{.}4s.(3$ Points$)$

$a=\frac{dv}{de{l}_t}$

$N=v_0+$act

$S=S_0+v_{0}t+\frac{1}{2}ac{t}^2$

b$)$

$V=v_0+\frac{1}{2}(-12\frac{n}{s})(t^2)$

$=\frac{1}{2}(-12\frac{m}{s})(t^2)$

$=-6\frac{m}{s}(t^2)$

$\sqrt[\phantom{2}]{6}=\sqrt[\phantom{2}]{t^2}$

$2\mathrm{.}45s=t$