5.2 How to calculate thinking distances and braking distances from velocity - time graphs

Graphs 1a

You have probably encountered velocity time graphs by now, so you should know that the area under a section of a velocity- time graph is equal to the distance travelled in that section (in terms of units m/s x s = m).

The graphs assume the same car and driver so that the deceleration on maximum braking is the same, which is why the negative gradient is the same value on both graphs.

 

The graph on the left of 1a shows an initial situation of a driver's quicker response time travelling at a lower speed.

Rectangular area A1 = initial velocity v1 x reaction time t1 = thinking distance

The area A1 is equal to the thinking distance, that is the distance the vehicle travels in the time it takes the driver to respond to a situation and starts to apply the brakes.

Right angled triangular area A2 = ½  x initial velocity v1 x braking time t2 = braking distance

The area A2 is the braking distance, that is the distance the vehicle travels from its maximum initial speed, when braking starts, until it comes to a halt.

The total area = A1 + A2 = stopping distance

 

The graph on the right of 1a shows a driver's slower reaction and the vehicle is moving at a greater speed.

This means two factors have been changed to emphasise how stopping distance is so easily and dramatically  increased.

So v2 > v1 and times t1 and t2 are both increased, so both areas A1 and A2 are increased.

The purple shaded areas indicate the increase in thinking distance A1 and braking distance A2.

This might mean lack of care and attention e.g. tired and not concentrating on the speed limit.

Rectangular area A1 = initial velocity v2 x reaction time t1 = thinking distance

Right angled triangular area A2 = ½  x initial velocity v2 x braking time t2 = braking distance

So, both area A1 and A2 are greatly increased, increasing the likelihood of an accident if driving carelessly!

The total area = A1 + A2 = stopping distance, and much greater than before.

 

 If you have followed the above logical arguments, you should be able to interpret the graphs if only one factors was changed.

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INDEX of physics notes on reaction times, stopping distances of road vehicles, Newton's 2nd Law, braking friction force, KE calculations