How Long Does It Take for One Car to Overtake Another?

[Demio Crush]

question : a car traveling at constant speed 20m/s overtakes another car which is moving at constant acceleration of 2 m/s^2 and it’s initially at rest . assume the length of each car to be 5 meters . thetotal road distance used in overtaking is ...

my attempt : for overtaking , t = distance between car 1 and car 2 + 5+5+5 / 20-2t
20-2t is the average velocity .
with this I get a quadratic equation , which I had to solve by formula method . But , for my method 2 variables are unknown .

Been trying this problem for past 2 hours . help please . I'll be really glad .

 

[C. Lee]

question : a car traveling at constant speed 20m/s overtakes another car which is moving at constant acceleration of 2 m/s^2 and it’s initially at rest . assume the length of each car to be 5 meters . thetotal road distance used in overtaking is ...

my attempt : for overtaking , t = distance between car 1 and car 2 + 5+5+5 / 20-2t
20-2t is the average velocity .
with this I get a quadratic equation , which I had to solve by formula method . But , for my method 2 variables are unknown .

Been trying this problem for past 2 hours . help please . I'll be really glad .

Doesn't the problem give the initial distance between two cars?

 

[BvU]

Hi Demio, welcome to PF !

Please use the template. Its use is mandatory in PF; check the guidelines to see why.

Make a few sketches to judge the situation. Position of the front of car 1 and 2 as a function of time. The identify the variables you need to describe it and collect enough equations to solve. If there are two unknowns, there must be two equations as well, or else you can't solve it.

 

[BvU]

Doesn't the problem give the initial distance between two cars?

It does.

 

[insightful]

Define "overtakes." I would say it means "gets ahead by a nose" or basically side-by-side.
Tip: Reserve t for time. Use s or x for distance.

 

[BvU]

Demio ?