$A$ scooter starts from rest and moves in a straight line with a constant acceleration,covering a distance of $64 \, m$ in $4 \, s$.
$(i)$ Calculate its acceleration and its final velocity.
$(ii)$ At what time had the scooter covered half the total distance?
$(i)$ Calculate its acceleration and its final velocity.
$(ii)$ At what time had the scooter covered half the total distance?
(N/A) $(i)$ Given: Initial velocity $u = 0 \, m/s$,Distance $S = 64 \, m$,Time $t = 4 \, s$.
Using the equation of motion $S = ut + \frac{1}{2}at^2$:
$64 = 0(4) + \frac{1}{2} \times a \times (4)^2$
$64 = 8a$
$a = 8 \, m/s^2$.
Using the equation $v = u + at$:
$v = 0 + 8 \times 4 = 32 \, m/s$.
$(ii)$ Half the total distance is $S' = \frac{64}{2} = 32 \, m$.
Using $S' = ut + \frac{1}{2}at^2$:
$32 = 0(t) + \frac{1}{2} \times 8 \times t^2$
$32 = 4t^2$
$t^2 = 8$
$t = \sqrt{8} \approx 2.83 \, s$.
Using the equation of motion $S = ut + \frac{1}{2}at^2$:
$64 = 0(4) + \frac{1}{2} \times a \times (4)^2$
$64 = 8a$
$a = 8 \, m/s^2$.
Using the equation $v = u + at$:
$v = 0 + 8 \times 4 = 32 \, m/s$.
$(ii)$ Half the total distance is $S' = \frac{64}{2} = 32 \, m$.
Using $S' = ut + \frac{1}{2}at^2$:
$32 = 0(t) + \frac{1}{2} \times 8 \times t^2$
$32 = 4t^2$
$t^2 = 8$
$t = \sqrt{8} \approx 2.83 \, s$.
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