Calculating Distance and Velocity in a Moving Object Scenario

  • Thread starter Thread starter nblu
  • Start date Start date
  • Tags Tags
    Forces Motion
AI Thread Summary
A car accelerates from rest at 4.0 m/s² while a truck travels at a constant speed of 90.0 km/h (25 m/s). After 10 seconds, the car covers 200 meters, and the truck covers 250 meters. The car passes the truck at 312.5 meters, reaching a speed of 50 m/s at that point, taking 12.5 seconds to do so. Both vehicles, when braking uniformly from their respective speeds, will stop in time before hitting a barrier 100 meters away, as their stopping distances are less than 100 meters.
nblu
Messages
56
Reaction score
0
Regarding Forces & Motion (edited)

Hi, thank you for your time to read this thread.
I'll begin with the question, thanks again!

Q: At the instant a traffic light turns green, a car starts from the rest and accelerates
uniformly at a rate of 4.0 m/s^{2} East. At the same instant, a truck traveling with a
constant velocity of 90.0 km/h East overtakes and passes the car.

a) How far beyond the starting point is the car after 10.0 s?
b) How far beyond the starting point is the truck after 10.0 s?
c) The car passes the truck at a distance of 312.5m beyond the starting point.
How fast is the car traveling at this instant?
d) How long does the car take to pass the truck?
e) Both drivers suddenly see a barrier 100.0m away and hit their brakes at exactly
same time. Assuming that both vehicles decelerate uniformly and they take 3.0 s
to stop, will the stop in time?


*******************************
Here are my answers :)
A: (I've omit vector signs, not sure how to input the symbol)
a) a = 4.0 m/s^{2}, \Deltat = 10.0 s
\Deltad = (v)(t) + 1/2(a)(t^2)
\Deltad = (0)(10) + 1/2(4)(100)
\Deltad = 200m

b) v = 90.0 km/h (convert to m/s which equals to 25m/s), \Deltat = 10.0 s
\Deltad = (v)(t)
\Deltad = (25)(10.0)
\Deltad = 250m

c) \Deltad = 312.5m, a = 4.0 m/s^{2}
vii^{2} = vi^{2} + 2a\Deltad
vii = (0) + 2(4.0m/s^{2})(312.5m/s)
vii = 50 m/s

d) a = 4.0 m/s^{2}, vii = 50 m/s
\Deltat = (vii - vi) / a
\Deltat = (50m/s - 0) / 4.0 = 12.5 seconds

e) Here, what I thought of doing was, find both car and truck's acceleration
then find their distance within 3 seconds then check whether the answer is
higher than 100m or not.

***Car
a = \Deltav / t
a = 0 m/s - 50 m/s / 3.0s
a = -16.7 m/s^{2}

\Deltad = (vii)\Deltat - 1/2a\Deltat^{2}
\Deltad = 75.15m

***Truck
Same calculation
\Deltad = 37.35m

// So I've said that those two vehicles will stop on time because the calculated
distance is less than 100m.

-----------------

Thank you for reading this.. I really appreciate it.. It's very long..
I needed some advice especially on e), because that question really got me thinking.
I honestly don't have confidence that my answers are right :( If I'm wrong
please correct me XD

Thanks again!
 
Last edited:
Physics news on Phys.org
nblu said:
Hi, thank you for your time to read this thread.
I'll begin with the question, thanks again!

Q: At the instant a traffic light turns green, a car starts from the rest and accelerates
uniformly at a rate of 4.0 m/s^2 East. At the same instant, a truck traveling with a
constant velocity of 90.0 km/h East overtakes and passes the car.

a) How far beyond the starting point is the car after 10.0 s?
b) How far beyond the starting point is the truck after 10.0 s?

*******************************

For question a), is it be possible to use a = v/t equation to find the velocity
then use v=d/t to find the final answer?

I was wondering if the same thing happens for question b) it looks much simpler
if use v=d/t equation.


Any advice would be appreciated, many thanks!

a) It may be using complex math, but otherwise no.
how about using the formula s=v_i t+\frac{at^2}{2}

b)You know it's velocity, which is constant, so how would you calculate distance over a certain time interval?

Remember to use SI units.
 
malty said:
a) It may be using complex math, but otherwise no.
how about using the formula s=v_i t+\frac{at^2}{2}

b)You know it's velocity, which is constant, so how would you calculate distance over a certain time interval?

Remember to use SI units.

So the V in that equation represents the initial, which is 0 right? t would be the given unit
in the question and same for b)

Thanks!
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top