A scooterist trying to overtake truck

[rudransh verma]

Homework Statement

A pickup vehicle is moving with a speed of 15.00 m/s on a straight road. A scooterist wishes to overtake the pickup vehicle in 150.0 s. If the pickup vehicle is at an initial distance of 1.500 km
from the scooterist, with what constant speed should the scooterist chase the pickup vehicle?

Relevant Equations

xp (distance of pickup truck from origin)= x0 + xs (distance of scooter from origin).

If 150s is the time in which overtaking has to occur then why are they using this eqn: xp=x0+xs.

 

[anuttarasammyak]

I prefer, how much speed of the scooterist does the driver of pick up observe in his behind?

 

[rudransh verma]

I prefer, how much speed of the scooterist does the driver of pick up observe in his behind?

I am thinking if we use v= u+ at and s=ut +halfatsquare. Take a to the lhs in both eqns and equate rhs. But my answer was wrong.
Other approach is to take vs*t=x0 where vs is to be found out. t is given and x0 (1.5km)is also given. But my answer was wrong.

 

[Delta2]

I am thinking if we use v= u+ at and s=ut +halfatsquare. Take a to the lhs in both eqns and equate rhs. But my answer was wrong.

These equations are for uniform acceleration. The problem states clearly that the skuter will move with constant velocity.

Other approach is to take vs*t=x0 where vs is to be found out. t is given and x0 (1.5km)is also given. But my answer was wrong.

This would be correct if the velocity of the truck was zero. You should correct the above equation by adding something to $x_0$. What is that? Try to think that while the skuter is moving to catch up the truck, the truck is also moving.

 

[rudransh verma]

This would be correct if the velocity of the truck was zero. You should correct the above equation by adding something to x0.

Ok! So we need to cover a distance equivalent to x0 + the distance covered by truck in 150s ie xst=x0+xpt ?
The question is not about constant acceleration. Both vehicles are moving at constant speed at all time.
what is the starting point of the vehicles from origin?

 

[Delta2]

You can take the origin to be anywhere and the starting points anywhere but with one restriction: Their in between distance must be 1.500Km. For convenience you can put the origin at the starting point of the skuter, at least that's how I think about this problem.

 

[kuruman]

Other approach is to take vs*t=x0 where vs is to be found out. t is given and x0 (1.5km)is also given. But my answer was wrong.

That equation would work if the pickup vehicle were not moving. Because it's moving, the scooterist will catch up with it farther down the road than 1500 m. How much farther?