The car will catch the truck after 14 seconds.
Explanation:
The truck is travelling at constant speed, so we can write its position at time t as
[tex]x_t (t) = v t[/tex]
where
v = 28.0 m/s is the speed of the truck
On the other hand, the police car is accelerating from rest, therefore its position at time t is given by
[tex]x_c(t) = \frac{1}{2}at^2[/tex]
where
[tex]a=4.0 m/s^2[/tex] is the acceleration of the car
The car will catch the truck when the two positions are identical:
[tex]x_t(t) = x_c(t)[/tex]
Solving for t,
[tex]vt=\frac{1}{2}at^2\\t=\frac{2v}{a}=\frac{2(28)}{4.0}=14 s[/tex]
Therefore, the car will catch the truck after 14 seconds.
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