Question

Derive: s = ut + 1/2 at2
​

Answer 1

Answer

Question

(a) Derive the formula:

s

=

u

t

+

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.

Solution

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

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