The velocity of a train is reduced uniformly from 40km/sec while travelling a distance of 100km.
A. Calcukate the retardation.
B. How much farther will it trqvel before coming to rest, assuming the same retardation.
surely you mean 100 m not 100 km
and 40 m/s not km/s (40,000 meters per second is quite a train)
and what is the final speed ?
v = Vi + a t
d = Vi t + (1/2)a t^2
v = 40 + a t ...... whatever v is so a = (v-40)/t
( a is negative of course)
use that in
100 = 40 t + (1/2) a t^2
solve for t and go back and get a
then do for v = 0 to find stopping distance
First, do you mean 40km/sec? That's one fast train.
Maybe you meant 40 m/s. That's about 144 km/hr. More likely.
Or, even better, maybe 40 km/hr = 17.88 m/s
Now, the real problem is, you don't say how long it takes to cover that distance, nor what its velocity then was. So there's no way to find the acceleration. And no way to extrapolate to when v=0.
In any case, you just have to use
s(t) = vt + 1/2 at^2
to solve this problem.
Ikr that's why I wasn't getting the answer. Thanks.
To calculate the retardation of the train, we need to use the formula:
retardation = change in velocity / time taken
A. Calculation of retardation:
Given:
Initial velocity (u) = 40 km/hr
Final velocity (v) = 0 km/hr
Distance (s) = 100 km
We need to find the retardation.
First, we need to convert the velocities to meters per second since the SI unit of velocity is m/s.
40 km/hr = (40 * 1000) / (60 * 60) m/s = 11.11 m/s
0 km/hr = 0 m/s
Now, we can calculate the retardation:
retardation = (v - u) / t
Since the velocity is reducing uniformly, the time taken (t1) to travel the given distance can be calculated using the formula:
s = ut + (1/2)at^2
Here, s = 100 km = 100,000 m (converting to meters)
u = 40 km/hr = 11.11 m/s (as calculated above)
a = retardation (to be found)
t1 = time taken to travel the given distance
Using the above formula, we can solve for t1:
100,000 = 11.11 * t1 + (1/2) * a * t1^2
Simplifying the equation:
100,000 = 11.11t1 + 0.5at1^2
Since the velocity is coming to rest, the final velocity (v) is 0. Therefore, the time taken to come to rest (t2) can be calculated using the formula:
v = u + at
Using the values given: 0 = 11.11 + a * t2
Now, we have two equations:
Equation 1: 100,000 = 11.11t1 + 0.5at1^2
Equation 2: 0 = 11.11 + a * t2
We can use these two equations to solve for the retardation (a).
B. Calculation of the distance traveled before coming to rest:
To calculate the distance traveled before coming to rest, we can use the formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Using the same acceleration (retardation) obtained from part A and the time taken to come to rest, we can calculate the distance.
Now, using the equations, we can find the answer to both parts A and B.