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Question

A cyclist is traveling at 15m/sec. She applies brakes so that she does not collide with a wall 18 metre away. What deacceleration must she have?  


Solution

In this question we will calculate the negative acceleration/deceleration, as follows:

Kinematic equations:

SUVAT-- s-displacement, u-initial velocity, v-final velocity,a- acceleration, t-time
v=u + at
v^2 = u^2 + 2as
s=1/2(u+v)t
s=ut + 1/2at^2

Her initial velocity, u is 15m/s
Her final velocity is, v 0m/s (since she stops)
Displacement is, s 18m
Hence the acceleration, a :

v^2=u^2 + 2as

0=15^2 + 2 x a x 18
0=225 + 36a
36a= -225

a =  -225/36
a= -6.25 m/s/s

Therefore she has to decelerate at the rate of 6.25m/s2

 

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