CHAPTER 21. MOTION IN ONE DIMENSION 21.7
∆~x = ~vi(~vf−~vi
a)
+^12 a(~vf−~vi
~a) 2
= ~vi~a~vf−~v(^2) i
~a+^12 ~a
(~vf (^2) − 2 ~vi~vf+~v (^2) i
~a^2
)
= ~vi~a~vf−~~v(^2) i
~a+
~vf^2
2 ~a−
~vi~vf
~a +
~v^2 i
2 ~a
2 ~a∆~x = − 2 ~v^2 i+~v^2 f+~v^2 i
~vf^2 = ~vi^2 + 2~a∆~x
This gives us the final velocity in terms of the initial velocity, acceleration and displacement
and is independent of the time variable.
Applications in the real-world ESAHI
What we have learnt in this chapter can be directly applied to road safety. We can analyse
the relationship between speed and stopping distance. The following worked example
illustrates this application.
Example 9: Stopping distance
QUESTION
A truck is travelling at a constant velocity of 10 m·s−^1 when the driver sees a
child 50 m in front of him in the road. He hits the brakes to stop the truck. The
truck accelerates at a rate of -1.25 m·s−^2. His reaction time to hit the brakes is 0,5
seconds. Will the truck hit the child?
SOLUTION
Step 1:Analyse the problem and identify what information is given
It is useful to draw a time-line like this one:
Physics: Mechanics 433