Answer
part (d)
Work Step by Step
a) Substitute different values of t like t=0, 0.5, 1 and so on and plot the trajectory. See the trajectory below.
(b)
$\vec{v} = v_x\hat{i}+v_y\hat{j}$
$\vec{v} = \frac{dx}{dt}\hat{i}+\frac{dy}{dt}\hat{j}$
$\vec{v} = \alpha \hat{i} - 2\beta t\hat{j}$
$\vec{a} = \frac{d\vec{v}}{dt} = -2\beta \hat{j}$
(c)
At t=2s
$\vec{v} = 2.4\hat{i}-4.8\hat{j}$
So, $|\vec{v}| = 5.37m/s$
at an an angle of $63^o$ downward with the x axis.
$\vec{a} = -2.4\hat{j}$
$|a| = 2.4m/s^2$
in the downward direction
(d)
As we can the y component of velocity is negative and the acceleration is also negative in the y-direction. So overall the y component of the velocity will become more negative with time and since speed is the magnitude of velocity so speed increases.
