Cars problem

[BobbyJones]

Two cars are at the start lines of two roads at right angles to each other and pointing towards the cross-road intersection 500 m away. Car A starts from rest with uniform acceleration of 0·5 m/s² and accelerates for 20 seconds. It then continues at the speed reached. Car B starts 5s later and 20m further back from the start distance of car A with an acceleration of 0·7 m/s².



calculate, with respect to start time of car A :-

a. The time it takes for B and A to be at the same distance from the
cross-roads.



Can someone start me off. I got Car A velocity at 10 m/s, and accelerated for 100m, leaving 400 meters left. I Used the formula S + 20 = ut + 0.5x0.7x(t-5)^2 But think I'm going worng.


The rest of the question says:

i. The distance from the cross-roads at the above time.
ii. The average velocity of car A at this distance


c. Car B stops accelerating at this point and continues at the speed reached What is the shortest distance between the two cars as they pass the cross roads.


It's a nice question, however I cant seem to do it yet, if you can, please explain how.

 

[Deleted member 4993]

Two cars are at the start lines of two roads at right angles to each other and pointing towards the cross-road intersection 500 m away. Car A starts from rest with uniform acceleration of 0·5 m/s² and accelerates for 20 seconds. It then continues at the speed reached. Car B starts 5s later and 20m further back from the start distance of car A with an acceleration of 0·7 m/s².



calculate, with respect to start time of car A :-

a. The time it takes for B and A to be at the same distance from the
cross-roads.



Can someone start me off. I got Car A velocity at 10 m/s, and accelerated for 100m, leaving 400 meters left. I Used the formula S + 20 = ut + 0.5x0.7x(t-5)^2 But think I'm going worng.


The rest of the question says:

i. The distance from the cross-roads at the above time.
ii. The average velocity of car A at this distance


c. Car B stops accelerating at this point and continues at the speed reached What is the shortest distance between the two cars as they pass the cross roads.


It's a nice question, however I cant seem to do it yet, if you can, please explain how.

The problem statement is ambiguious to me. In the first line it states:

Two cars are at the start lines of two roads at right angles to each other and pointing towards the cross-road intersection 500 m away.

To me it says both the cars are 500 m away (equal distance). Then further down it states:

Car B starts 5s later and 20m further back...

So now my question is - which car was 500m away from the cross-road? Which car is 520m (or 480 m) away from the cross-road?

Either way:

the car A travels 100 m in first 20 sec (S = 1/2 * 0.5 * 20² = 100)

In that time the car B travels 78,75 m (S = 1/2 * 0.7 * 15² = 78.75)

Now calculate their respective speeds and distances to be be covered and continue.....

 

[BobbyJones]

Car A is at 500m away from the intersection, and car be is 520 meters away from the intersection.

The question says that car A accelerates for 20 second and then travels at a constant velocity of 10m/s. However for car B it dosent say how long it accelerates, only by how much, 0.7m/s. Do you think I'm to take it as 15 seconds??


Subhotosh;
car A has 400m remaining at 10m/s, therefore it'll take 40 seconds to get to the cross roads
car be will be 520 - 78.75m = 441.25m away from the cross roads.

How do I work out the speed for car B? with no more information?

Is it

B = A
441/x = 400/10

x = 11.025 m/s

Am I getting lost?