Question

(a) Derive the formula: $s=ut+\frac{1}{2}a{t}^2$, 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.

Answer 1

a)To Prove,
S = ut + (1/2)at²
Where, S = Diatance
u = Initial Velocity
a = acceleration
t = time.

Proof :
Acceleration = (Final velocity - Initial Velocity)/t
a = (v - u)/t
at = v - u -------------------------------eq(i)

Now, We know,
Distance Traveled = Average Velocity × Time
S = (v + u)/2 × t

But From eq(i) , v = u + at
S = (u + at + u)/2 × t
S = [(2u + at)/2] × t
⇒ S = ut + (1/2)at²
b)If a train starts from stationary position then initial velocity of train = 0

moving uniform acceleration means constant acceleration.

given ,
final velocity ( V) = 36 km/h = $36\times \frac{5}{18}$ = 10m/s $1\frac{km}{hr}=\frac{5}{18}\frac{m}{s}$

time taken = 10 minutes = 10 × 60sec = 600sec

use kinematics equation ,

V = u + at

10 = 0 + a × 600

a = 10/600 = 1/60 m/s²

a = m/s² = m/s²