Velocity? In general physics, please help me. thanks its about kinematics,

Question

In general physics, please help me. thanks

its about kinematics,

1) a police car is searching for a fugitive that managed to escape a while ago. knowing that he is now safe, the fugitive begins to take a rest until he notices a police car approaching him at 10 meter/sec, accelerating at 5 meter/sec^2 and it is 100meters away. the fugitive grabs a motorcycle and starts it accelerating at the same rate as the police car. how much time will it take the police car to catch the fugitive?

2) a car starts from rest and moves along a straight line with an acceleration of a=(3 u^(-1/3)) meter/sec^2, where "u" is in meters? determine the car's velocity and position when t=10s.

--pls help me guys,

Answer 1

1) Let x1 and x2 be the positions of the car and the motorcycle at t=0.

Let v1 and v2 be the speeds of the car and the motorcycle at t=0.

At t=0 --> x1= -100 m, x2=0, v1=10 m/s, v2=0

car:  x= x1+v1*t+0.5*at^2

x= -100+10t+0.5*5t^2

motor: x= x2+v2*t+0.5*at^2

x=0.5*5t^2

The police will catch the fugitive --> x=x

-100+10t+0.5*5t^2=0.5*5t^2

10t=100

t=10 s

2)

v=at=[3*u^(-1/3)]*t=3u^(-1/3)*t

x=0.5at^2=0.5[3*u^(-1/3)]*t^2

x=1.5*u^(-1/3)*t^2