Q$.1($a$)$ A car departs from Location A to Location B from rest and accelerates

uniformly to a velocity of $70k\frac{m}{?}$ hour in $1$ minute. Then, the car decelerates

uniformly to Location C and travelled $800m$ from Location B to C$.$ The

velocity of the car when it arrives Location $C$ is $45k\frac{m}{?}$ hour. Then, the car

moves to Location D with the same acceleration of that from Location A to B

for $1\mathrm{.}25$ minutes. Finally, the car uses another $2\mathrm{.}5$ minutes to decelerate

uniformly to Location $E$ and then stops. A relevant velocity$-$time graph is

shown in Figure Q$\mathrm{.}1($a$)$ below.

$($i$)$ Calculate the acceleration and deceleration $(\frac{m}{s^2})$ of the car when it

departs from Location A to Location B$,$ Location B to C$,$ Location C to D

and Location D to E; and

$(5$ marks$)$

$($ii$)$ the total distance $($m$)$ travelled from $A$ to $E.$

$(5$ marks$)$

$($b$)$ A man stands on the roof of a building of $200m$ height and drops a coin that

reaches the ground while another man throws a ball upward from the ground

with a velocity of $50\frac{m}{s}$ at the same instant.

$($i$)$ the time $($s$)$ and velocity $(\frac{m}{s})$ when the coin strikes the ground;

$(4$ marks$)$

$($ii$)$ the time $($s$)$ and height from ground $($m$)$ when the velocity of ball is $0$

$\frac{m}{s}$; and

$($iii$)$ the time $($s$)$ and height from ground $($m$)$ when coin and ball meet together.

$(7$ marks$)$