Question

What is stopping distance for vehicle ? On what factors, does it depend ? Derive the equation for stopping

distance.​

Answer 1

Stopping Distance:

• The distance needed for an object (in motion) to become stationary (i.e. stop moving) is called STOPPING DISTANCE.

Dependent Factors :

The various factors on which the stopping distance depends are :

• Initial velocity of car
• Mass of car
• Coefficient of friction between tyre and road
• Gravitational acceleration at that place

Derivation of stopping distance:

Let's assume that the car was moving with initial velocity of u and mass of car is m.

Applying EQUATIONS OF KINEMATICS:

$\rm {v}^{2} = {u}^{2} + 2as$

• Since the car stopped, the value of 'v' should be 0.

$\rm \implies {0}^{2} = {u}^{2} + 2as$

$\rm \implies 2as = - {u}^{2}$

$\rm \implies s = \dfrac{ - {u}^{2} }{2a}$

• Now, acceleration is written as Frictional force/mass

$\rm \implies s = \dfrac{ - {u}^{2} }{2 \times \dfrac{ \mu mg}{m} }$

$\boxed{ \rm \implies s = \dfrac{ - {u}^{2} }{2 \times \mu g } }$

Hope It Helps.