Answer: 10 s, 30 m/s , 150 m
Explanation:
Given
The speed of motorcyclist is [tex]u_1=15\ m/s[/tex]
The initial speed of a police motorcycle is [tex]u_2=0\ m/s[/tex]
acceleration of police motorcycle is [tex]a=3\ m/s^2[/tex]
Police will catch the motorcyclist when they traveled equal distances
distance traveled by motorcyclist in time t is
[tex]\Rightarrow s_1=15\times t[/tex]
Distance traveled by Police in time t is
[tex]\Rightarrow s_2=u_2t+\frac{1}{2}at^2\\\Rightarrow s_2=0+0.5\times 3\times t^2[/tex]
put [tex]s_1=s_2[/tex]
[tex]\Rightarrow 15t=0.5\times 3\times t^2\\\\\Rightarrow t(1.5t-15)=0\\\\\Rightarrow t=\dfrac{15}{1.5}=10\ s[/tex]
Police officer's speed at that time is
[tex]\Rightarrow v_2=u_2+at\\\Rightarrow v_2=0+3\times 10=30\ m/s[/tex]
Distance traveled by each vehicle is
[tex]\Rightarrow s_1=s_2=15\times t=15\times 10=150\ m[/tex]
