Question

A truck is traveling at constant speed of t v =21 m/s is at x= (80, 100, 120, 140, 160) m in front of a police car moving with constant speed of p v =25 m/s. What is the time (in s) needs the police to catch the truck?

Answer 1

Answer:

t= (20, 25, ...  40) s

Explanation:

This is an exercise in kinematics specifically of uniform motion, the first thing we must do is set a reference system, we place our zero in the police car, we write the equations

police car

         x₁ = v₁ t

truck

         x₂ = x₀ + v₂ t

In this case, they indicate several initial positions of the truck and the speed of the two vehicles, at the meeting point the positions must be the same

         x₁ = x₂

        v₁ t = x₀ + v₂ t

        t (v₁ - v₂) = x₀

        t = $\frac{x_{o} }{v_{1}- v_{2} }$

let's calculate for each initial position

x₀ = 80m

      t = 80 / (25-21)

      t = 80/4

      t = 20 s

x₀ = 100 m

      t = 100/4

      t = 25 s

the last x₀ = 160 m

      t = 160/4

      t = 40 s

we can see that the time increases as the distance between the vehicles increases