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A car driver going at speed v suddenly finds a wide wall at a distance r.Should he apply brakes or turn the car in a circle of radius r to avoid hitting the wall?

A car driver going at speed v suddenly finds a wide wall at a distance r.Should he apply brakes or turn the car in a circle of radius r to avoid hitting the wall?

Grade:

1 Answers

Vasantha Kumari
askIITians Faculty 38 Points
7 years ago
Let us analyse the current situation in two aspects:
Car Turning in a Circle:
In this case speed does not change but velocity is changing and given by acceleration,
a = v2/r
Here, the needed acceleration for the car driver to avoid the wall in front is the square of the speed divided by the radius which is just the initial distance to the wall.
Car Applying Brakes:
Here, velocity does not change but the speed changes. So, if a is the acceleration, v0 the initial velocity, t the elapsed time then
x = 1/2 at2 + v0t + x0...(1)
and velocity
v = at +v0 ...(1)
If tf is the time corresponding to when car stopped,
eqn(2) becomes
tf= –v0/a...(3)
putting (3) in (1), we have
a = –v02 / 2r ...(4)
So, when you compare acceleration for the car driver taking curve, it is double than when he applies brakes.
Hence, it is better the car driver applies brakes to avoid hitting the wall

Thanks & Regards,

Vasantha Sivaraj,

askIITians faculty


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