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# a police man is running toward a thief with a constant acceleration of 0.1 m/s^2. At a particular instant t=0,the policeman is 20 m behind the thief and at the instant the velocity of policeman is 4 m/s. At this instant the thief observed the policeman coming  towards him. So he starts running away from the policeman in the same direction with a constant acceleration.Then what is the minimum acceleration with which the thief should run so that he is'nt caught

28 Points
one year ago
Firstly, we will find the distance between the theif and policeman.
⇒Usual speed = Speed of policeman - Speed of theif
⇒ Usual speed = 15 - 10
⇒Usual speed = 5 km/h
Now, we will change km/h into m/s
⇒Usual speed = 5 * (5/18)
⇒Usual speed = 25/18 m/s
___________________________
Distance covered = 400 m
Speed = 25/18 m/s
\Large{\star{\boxed{\sf{Time = \dfrac{Distance}{Speed} }}}}⋆
Time=
Speed
Distance
\begin{lgathered}\sf{\implies Time = \dfrac{400}{\dfrac{25}{18}}} \\ \\ \sf{\implies Time = \cancel{400} \times \frac{18}{\cancel{25}}} \\ \\ \sf{\implies Time = 16 \times 18} \\ \\ \sf{\implies Time = 288 \: seconds}\end{lgathered}
⟹Time=
18
25
400
⟹Time=
400
×
25
18
⟹Time=16×18
⟹Time=288seconds
Now, we have now time in which The policeman catch the thief.
Speed of theif = 10 km/h = 50/18 m/s
Time taken = 288 s
\Large{\star{\boxed{\sf{Distance = Speed \times Time}}}}⋆
Distance=Speed×Time
\begin{lgathered}\sf{Distance = \dfrac{50}{\cancel{18}} \times \cancel {288}} \\ \\ \sf{\implies Distance = 50 \times 16} \\ \\ \sf{\implies Distance = 800 \: m}\end{lgathered}
Distance=
18
50
×
288
⟹Distance=50×16
⟹Distance=800m
Vibekjyoti Sahoo
145 Points
15 days ago
Firstly, we will find the distance between the theif and policeman.
⇒Usual speed = Speed of policeman - Speed of theif
⇒ Usual speed = 15 - 10
⇒Usual speed = 5 km/h
Now, we will change km/h into m/s
⇒Usual speed = 5 * (5/18)
⇒Usual speed = 25/18 m/s
___________________________
Distance covered = 400 m
Speed = 25/18 m/s
\Large{\star{\boxed{\sf{Time = \dfrac{Distance}{Speed} }}}}⋆
Time=
Speed
Distance
\begin{lgathered}\sf{\implies Time = \dfrac{400}{\dfrac{25}{18}}} \\ \\ \sf{\implies Time = \cancel{400} \times \frac{18}{\cancel{25}}} \\ \\ \sf{\implies Time = 16 \times 18} \\ \\ \sf{\implies Time = 288 \: seconds}\end{lgathered}
⟹Time=
18
25
400
⟹Time=
400
×
25
18
⟹Time=16×18
⟹Time=288seconds
Now, we have now time in which The policeman catch the thief.
Speed of theif = 10 km/h = 50/18 m/s
Time taken = 288 s
\Large{\star{\boxed{\sf{Distance = Speed \times Time}}}}⋆
Distance=Speed×Time
\begin{lgathered}\sf{Distance = \dfrac{50}{\cancel{18}} \times \cancel {288}} \\ \\ \sf{\implies Distance = 50 \times 16} \\ \\ \sf{\implies Distance = 800 \: m}\end{lgathered}
Distance=
18
50
×
288
⟹Distance=50×16
⟹Distance=800m
Thank You!!!!!!!