Question

Help me with the question in the image I provided​

Answer 1

Answer: 10 s, 30 m/s , 150 m

Explanation:

Given

The speed of motorcyclist is  $u_1=15\ m/s$

The initial speed of a police motorcycle is $u_2=0\ m/s$

acceleration of police motorcycle is $a=3\ m/s^2$

Police will catch the motorcyclist when they traveled equal distances

distance traveled by motorcyclist in time t is

$\Rightarrow s_1=15\times t$

Distance traveled by Police in time t is

$\Rightarrow s_2=u_2t+\frac{1}{2}at^2\\\Rightarrow s_2=0+0.5\times 3\times t^2$

put $s_1=s_2$

$\Rightarrow 15t=0.5\times 3\times t^2\\\\\Rightarrow t(1.5t-15)=0\\\\\Rightarrow t=\dfrac{15}{1.5}=10\ s$

Police officer's speed at that time is

$\Rightarrow v_2=u_2+at\\\Rightarrow v_2=0+3\times 10=30\ m/s$

Distance traveled by each vehicle is

$\Rightarrow s_1=s_2=15\times t=15\times 10=150\ m$