Physics Question - Acceleration

JOR...

Real World Physics

Chapter 7 - Acceleration


Exercise 7.5

Q9. A body leaves a point A and moves in a straight line with a constant velocity of 40 m/s. Ten seconds later another body which is at rest at A is given an acceleration of 2 m s-2 and moves in the same direction as the first body. How long does it take the second body to catch up with the first? How far from A does this occur?


Can anyone help me by doing this out step-by-step?

nobodythere

JOR... wrote:

Real World Physics
Q9. A body leaves a point A and moves in a straight line with a constant velocity of 40 m/s. Ten seconds later another body which is at rest at A is given an acceleration of 2 m s-2 and moves in the same direction as the first body. How long does it take the second body to catch up with the first? How far from A does this occur?

When they meet, their distances from A will be equal (s1 = s2)

Particle1:
t1 = t1
u1=40
s=s

Particle2:
t2 = (t1 - 10) (this means that when they meet, particle2 will have been travelling for ten seconds less than particle 1)
u2=0
a=2
s=s


Take particle 1:
s = ut + 1/2 at^2
s = 40t1 +0
s = 40t1

Take particle 2:
s = ut + 1/2 at^2
s = 0 + (1/2)(2) (t1-10)^2
s = (t1 - 10)^2
s = t1^2 - 20t1 +100

But s1=s2

40t1=t1^2 - 20t1 + 100
t1^2 - 60t1 + 100 = 0


And solve the quadratic. At least I think that's right

*Angel*

1st Body:
Speed (v) = 40m/s
time (t) = 10 + t
Distance (s) = s

2nd Body:
Acceleration (a) = 2m/s^2
Initial Speed (u) = 0 m/s
Time (t) = t
Distance (s) = s

From Distance = speed x time, s = 40(10 + t)
= 400 + 40t

From s = ut + 1/2at^2, s = t^2

400 + 40t = t^2
t^2 - 40t - 400 = 0

Using the - b formula... you should get about 48seconds... (hopefully I'm not wrong). From there distance should be easy enough to calculate.

*Angel*

Hmm grasshopa beats me to it.

JOR...

No he didn't beat you to it. The answer can only be gained by letting one time equal T+10 and the other equal T. Somehow it doesn't work if you let one equal T and the other T-10.
This is why I had problems. I tried the T-10 way and the -b formula doesn't work (you get 30 'plus or minus' ( (square root) (20 'root' 2)). This gives you 8s or 58s which is wrong.
Then I thought of letting one equal T+10 and the other T but I thought I would end up getting the same answer. But thanks *Angel*.
I still don't understand why one works and the other doesn't though.

*Angel*

Both ways DO work... except the question was to find the time taken for the second body to catch up with the first. If you take away the extra 10 seconds from grasshopa's answer it is the same.

JOR...

Oh yeah sorry didn't notice that!