Question

There are two moving objects - graphs of t make angles of 30 and 45 along the time axis, get the ratio of their acceleration.​

Answer 1

Given :

For object A :

• Angle inclined by straight line with time axis = 30°

For object B :

• Angle inclined by straight line with time axis = 45°

To Find :

Ratio of their acceleration.

Solution :

❒ Acceleration is defined as the ratio of change in velocity to the time taken.

Mathematically, a = ∆v / ∆t

• It is a vector quantity having both magnitude as well as direction.
• SI unit : m/s²

We know that, slope of velocity → time gives us magnitude of acceleration.

$\dag\:\underline{\boxed{\bf{\purple{a=\dfrac{\Delta v}{\Delta t}=slope\:(m)=tan\:\theta}}}}$

By substituting the given values;

$\sf:\implies\:\dfrac{a_1}{a_2}=\dfrac{tan\:\theta_1}{tan\:\theta_2}$

$\sf:\implies\:\dfrac{a_1}{a_2}=\dfrac{tan\:30^{\circ}}{tan\:45^{\circ}}$

$\sf:\implies\:\dfrac{a_1}{a_2}=\dfrac{1/\sqrt3}{\sqrt3}$

$:\implies\:\underline{\boxed{\bf{\gray{a_1:a_2=1:3}}}}$