(a) Derive the formula: s = ut + ½ at² where the symbols have usual meanings. (b) A train starting from stationary position and moving with uniform acceleration attains a speed of 36 km per hour in 10 minutes. Find its acceleration.
By BYJU'S Exam Prep
Updated on: September 13th, 2023
(a) We have to prove that
s = ut + 1/2 at2
Where
s is the distance
u is the initial velocity
a is the acceleration
t is the time
Proof –
Acceleration = (Final velocity – Initial velocity)/t
a = (v – u)/ t
at = v – u …. (1)
We know that
Distance traveled = average velocity x time
s = (v + u)/ 2 x t
Using equation (1)
s = (u + at + u)/2 x t
s = [(2u + at)/ 2] x t
s = ut + 1/2 at2
(b) If a train starts from a stationary position, initial velocity = 0
Uniform acceleration refers to constant acceleration
It is given that
Final velocity V = 36 km/h = 36 x 5/18 = 10 m/s [As 1km/hr = 5/18 m/s]
Time taken t = 10 minutes= 10 x 60 = 600 seconds
From the kinematics equation
V = u + at
10 = 0 + a x 600
a = 10/600
a = 1/60 m/s2
a = 0.1667 x 10⁻1 m/s2 = 1.67 x 10⁻2 m/s2
Therefore, the formula is derived and the acceleration is 1.67 x 10⁻2 m/s2.
Summary:
(a) Derive the formula: s = ut + 1/2 at2 where the symbols have usual meanings. (b) A train starting from a stationary position and moving with uniform acceleration attains a speed of 36 km per hour in 10 minutes. Find its acceleration.
(a) The formula: s = ut + 1/2 at2 where the symbols have usual meanings is derived
(b) A train starting from a stationary position and moving with uniform acceleration attains a speed of 36 km per hour in 10 minutes. Its acceleration is 1.67 x 10⁻2 m/s2.
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