Acceleration Physics
Discussion
I've read the following on another forum:
Imagine you have two cars - one following the other, say, 20 feet behind at 10mph. They both have identical acceleration characteristics and they both hit the throttle at the same time. They carry on accelerating until they reach 70mph. At this point the trailing car is now 140 feet behind. Elementary Newtonian physics.
Before I reply to it the vein that it's complete borrocks, can the wise and wiser confirm my analysis please.
Imagine you have two cars - one following the other, say, 20 feet behind at 10mph. They both have identical acceleration characteristics and they both hit the throttle at the same time. They carry on accelerating until they reach 70mph. At this point the trailing car is now 140 feet behind. Elementary Newtonian physics.
Before I reply to it the vein that it's complete borrocks, can the wise and wiser confirm my analysis please.
Think about time.
You stand by the road and watch the first car go by at 20mph. You start a timer and stop it when the other car goes by. For simplicity let's say it was five seconds.
Now you stand further down the road, and do the same as they go past at 70mph. What do you think the time difference will be, given that they accelerated identically?
With that in mind, what's the distance between them?
You stand by the road and watch the first car go by at 20mph. You start a timer and stop it when the other car goes by. For simplicity let's say it was five seconds.
Now you stand further down the road, and do the same as they go past at 70mph. What do you think the time difference will be, given that they accelerated identically?
With that in mind, what's the distance between them?
Here's the reverse situation, distance between two cars under braking:
trashbat said:
Think about time.
You stand by the road and watch the first car go by at 20mph. You start a timer and stop it when the other car goes by. For simplicity let's say it was five seconds.
Now you stand further down the road, and do the same as they go past at 70mph. What do you think the time difference will be, given that they accelerated identically?
With that in mind, what's the distance between them?
time diff will be 5secs/(70/20) = 1.43secs, distance will be the sameYou stand by the road and watch the first car go by at 20mph. You start a timer and stop it when the other car goes by. For simplicity let's say it was five seconds.
Now you stand further down the road, and do the same as they go past at 70mph. What do you think the time difference will be, given that they accelerated identically?
With that in mind, what's the distance between them?
Yes, it's big hairy borrocks.
s = ut + 0.5at^2 for both cars (s = displacement, u = initial velocity, a = acceleration, t = time)
so for car 1:
s1 = u1*t + 0.5*a1*t^2
for car 2:
s2 = u2*t + 0.5*a2*t^2
We are told that initial velocity and acceleration are the same, hence:
u1 = u2 and a1 = a2
Time elapsed is equal as they both hit the throttle at the same time, so t is the same in both equations. So:
u1*t + 0.5*a1*t^2 = u2*t + 0.5*a2*t^2
Therefore, s1 = s2 ; the cars have both travelled the same distance for any given t, so any gap between the cars remains constant.
Apologies for the formatting.
s = ut + 0.5at^2 for both cars (s = displacement, u = initial velocity, a = acceleration, t = time)
so for car 1:
s1 = u1*t + 0.5*a1*t^2
for car 2:
s2 = u2*t + 0.5*a2*t^2
We are told that initial velocity and acceleration are the same, hence:
u1 = u2 and a1 = a2
Time elapsed is equal as they both hit the throttle at the same time, so t is the same in both equations. So:
u1*t + 0.5*a1*t^2 = u2*t + 0.5*a2*t^2
Therefore, s1 = s2 ; the cars have both travelled the same distance for any given t, so any gap between the cars remains constant.
Apologies for the formatting.
kambites said:
If they hit the throttle at the same time they stay the same distance apart.
If they hit the throttle at the same point on the road, the gap between them extends.
And if they decide to slow down behnd each other and hit the brakes at the same point on the road then the gap closes potentially resulting in a crashIf they hit the throttle at the same point on the road, the gap between them extends.
TATOR said:
I think the car behind would shorten the gap due to drafting off the one in front (but i really dont have a clue 
OK - let's do it properly, "two perfectly spherical vehicles, in a vacuum, and subject to no gravitational, frictional or other forces except those provided by their own propulsion systems...."Gassing Station | General Gassing | Top of Page | What's New | My Stuff