Question

A car and a bus have same speed. After applying brakes the bus stops earlier than the car. Is it because of inertia?​

Answer 1

Actually,

Read the answer carefully,

Only answer is not important but the concept behind the answer is important in physics problems,

So let they have same speed initially, V

Also let the masses be M(for bus) and m(for car), with M >m

Now,

Both have finally come to rest,

So final speed = 0

Now focus on the change in momentum,

Initially they had momentum

= MV (for bus) and mV (for car )

Finally they have momentum = 0 for both

So, change in momentum for bus is final momentum minus initial momentum = 0 - MV = - MV

and change in momentum for car is final momentum minus initial momentum = 0 - mV = - mV

Now if you consider the magnitude of the change in momentum you will find bus has more change in momentum and car has less change in momentum as MV > mV,

So, you know about force that it is change in momentum divided by time interval in which change occurred

Now there can be two cases :-

(1) Equal force is applied by breaks both in car and in bus,

So in this case,

F1= MV /t1 for bus

F2= mV /t2 for car

Since force is equal in both the case F1 = F2 , therefore as MV >mV => t1 > t2 for the ratio to be equal

So in this case bus takes more time to come to the rest (and your question is incorrect because you have said car takes more time but actually bus takes more time to stop)

And yes this is due to inertia

Inertia is nothing but the mass of the body, more is the mass more is the tendency to continue the state of the motion which is called inertia!

Case 2 :- They have to stop in equal time intervals,

So in this case,

F1= MV /t1 for bus

F2= mV /t2 for car

Now since t1 = t2,

Therefore, as MV > mV

F1 > F2,

So more force is needed to be applied by the breaks in case of the bus than the case of the car,

So here also Inertia plays the role as more is the mass, more is the inertia and hence more is the force required,

Actually your question is valid only for the case (1), for different forces and time intervals it is possible that either the bus stops earlier or the car stops earlier,

Answered by an IIT JEE ASPIRANT and all India mathematics OLYMPIAD TOPPER in class 10th

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