(a) if a train travelling at 72km/hr is to be brought to rest in a distance of 200m then wat should be its retardation
(b) if a body starts from rest and and travels 120 m in 8th sec then wats its acceleration.
(a) How do you define retardation?
Is it deceleration?
72 km/h = 20 m/s
Average velocity during deceleration = 10 m/s.
10*t = 200 m
Deceleration time t = 20 s
Deceleration rate = 20 m/s/20s
= 1 m/s^2
(b) If you are supposed to assume the acceleration rate is constant,
X(8) - X(7) = (a/2)*(64-49)
= 120
15*(a/2) = 120
a = 16 m/s^2
A motor car moving with a velocity of 54km/hr is brought to rest in (i) 5sec (ii) 3meter. Find the retardation in each case.
10*t = 200 m
this is wrong ????? because velocity is 20m/s
To answer these questions, we need to use the equations of motion. There are four equations of motion we can use:
1. v = u + at
2. s = ut + (1/2)at^2
3. v^2 = u^2 + 2as
4. s = (u + v)t/2
where:
- v represents the final velocity
- u represents the initial velocity
- a represents the acceleration
- t represents the time taken
- s represents the displacement
(a) To find the retardation of the train, we need to calculate the acceleration. Given that the train's initial velocity (u) is 72 km/hr and it comes to rest in a distance (s) of 200 m, we can use equation 3.
Initially, we need to convert the initial velocity from km/hr to m/s by dividing it by 3.6.
u = 72 km/hr = (72 * 1000) m/3600 s = 20 m/s
Using equation 3 and rearranging it, we have:
0^2 (since the train comes to rest) = (20)^2 + 2a(200)
Simplifying the equation:
0 = 400 + 400a
400a = -400
a = -1 m/s^2
Therefore, the retardation of the train is 1 m/s^2.
(b) To find the acceleration of the body, we need to calculate it using the given information. The body starts from rest, so the initial velocity (u) is 0 m/s, the distance (s) is 120 m, and the time (t) is 8 sec. We can use equation 2.
Using equation 2:
120 = 0 * 8 + (1/2)a(8^2)
Simplifying the equation:
120 = 32a
a = 120/32
a ≈ 3.75 m/s^2
Therefore, the acceleration of the body is approximately 3.75 m/s^2.