First slide

The 3 equation for uniform acc

Question

A body starts from rest and moves with constant acceleration for t second. It travels a distance x₁ in first half of time and x₂ in next half of time, then

Moderate

A

x₂ = x₁
B

x₂ = 2x₁
C

x₂ = 3x₁
D

x₂ = 4x₁

Solution

a = constant
Let A be the original point.
From equation of motion,
$x = u t + \frac{1}{2} a t^{2} = \frac{1}{2} a t^{2}$ ( $∵$ u = 0)
For point C, $x_{1} = \frac{1}{2} a (t / 2)^{2} \Rightarrow x_{1} = \frac{1}{8} a t^{2}$
Distance travelled by the body in t second is
$x_{1} + x_{2} = \frac{1}{2} a (t)^{2} = 4 x_{1}$
$x_{2} = 4 x_{1} - x_{1} = 3 x_{1}$

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