Speed is a scalar quantity. So it's essentially positive.
cos (pi/3) = 1/2; sin (pi/3) = sqrt(3)/2
Velocity (x-direction) = vx = dx/dt = d/dt (4*t*cos(pi/3) = 4*(1/2) = 2 m/s
Since the velocity is positive, the velocity is also the speed.
Acceleration (x-direction) = ax = d(vx)/dt = 0
The horizontal velocity is constant.
Velocity (y-direction) = vy = dy/dt = d/dt (4*sin(pi/3)*t - 5*t^2) = 4*(sqrt(3)/2) - 10*t
After 1 second, vy = 2*sqrt(3) - 10(1) = -6.54 m/s
Since we're asking for speed (velocity is a vector), we must take the absolute value
Vertical Speed = abs(vy) = 6.54 m/s (downward)
Acceleration (y-direction) = ay = d(vy)/dt = -10 m/s^2
Neglecting air resistance, the gravitational acceleration is constant.
Ergo, acceleration does not with time.
Hope this helps.