A traffic police car travelling at 120km/hr is chasing a taxi 0.5 km away travelling at 100 km/hr. How far must the police car travel to catch up with the taxi?
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Answer:
Thus after 20s the police car catches the speeding car
Step-by-step explanation:
The origin of co ordinate system (x-axis), we assume it is the point where speeding car passes the police car
x
speeding
(t)=30t→1
The motion of the speeding car is the motion with constant speed of 30㎧
The motion of the police car is the motion with constant acceleration
∴x
police
(t)=v
initial
(t)+a
2
t
2
v(t)=v
initial
+at
v
2
(t)−v
initial
2
=2ax
police
(t)
a=3㎨
Initial velocity=0=v
initial
∴x
police
(t)=1.5t
2
→2
v(t)=3t
v
2
(t)=6x
police
(t)
x
speeding
(t
0
)=x
police
(t
0
)→3
Substituting equation 1,2
30t
0
=1.5t
0
2
t
0
=
1.5
30
=20s
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