Answer:
The statement is true: velocity and acceleration have opposite directions in the interval of braking.
Explanation:
Let's say we have a velocity [tex]v>0[/tex].
The acceleration [tex]a[/tex] is the rate of change of the velocity [tex]v[/tex]. This means that if [tex]v[/tex] is increasing during time, then [tex]a[/tex] must be positive. But if [tex]v[/tex] is decreasing over time, then [tex]a[/tex] will be negative (even though the velocity is positive).
Mathematically:
[tex]a=\frac{dv}{dt}[/tex]
[tex]v[/tex] decreases ⇒[tex]\frac{dv}{dt}<0[/tex]
⇒[tex]a<0[/tex].
Example:
[tex]v(t)=e^{-t}>0 \\\\\frac{dv}{dt}=-te^{-t} <0\\\\a<0.[/tex]
