Question

A body starts from rest and travels with uniform acceleration. If the distance covered in first \(2\) seconds is \(x\) and next \(2\) seconds is \(y\), then

• A. \(y=x\)
• B. \(y=2x\)
• C. \(y=3x\)
• D. \(y=4x\)

Hint:

For a body starting from rest with uniform acceleration, distances in successive equal time intervals are in the ratio \(1:3:5:\cdots\).

Answer 1

The Correct Option is C

The body starts from rest. So, \[ u=0. \] Let the uniform acceleration be: \[ a. \] Distance travelled in time \(t\) is: \[ s=ut+\frac{1}{2}at^2. \] Since \(u=0\), \[ s=\frac{1}{2}at^2. \] Distance covered in first \(2\) seconds: \[ x=\frac{1}{2}a(2)^2. \] \[ x=\frac{1}{2}a\cdot 4. \] \[ x=2a. \] Now distance covered in first \(4\) seconds: \[ s_4=\frac{1}{2}a(4)^2. \] \[ s_4=\frac{1}{2}a\cdot 16. \] \[ s_4=8a. \] Distance covered in next \(2\) seconds means distance from \(t=2\) to \(t=4\). So, \[ y=s_4-x. \] \[ y=8a-2a. \] \[ y=6a. \] Since \[ x=2a, \] we get: \[ y=3(2a). \] \[ y=3x. \] Hence, \[ y=3x. \]