Answer:
Explanation:
From the given information;
Let assume that the distance travelled by the speeder prior to the time the trooper catches with it to be = d
the time interval to be = t
Then, the speeder speed = distance/time
Making distance the subject; then:
distance (d) = speed × time
d = (50 m/s)t
d = 50 t --- (1)
Now, for the trooper; Using the equation of motion:
d = 20t + 1.25t²
Replace the value of d in (1) to the above equation, we have:
50 t = 20 t + 1.25t²
50t - 20t = 1.25t²
30t = 1.25t²
30 = 1.25t
t = 24 seconds
From (1), the distance far down the highway the trooper will travel prior to the time it catches up with the speeder is:
= 50t
= 50(24)
= 1200 seconds