Question #c9885

1 Answer
A08
Feb 7, 2017

#4.43ms^-1#, rounded to two decimal places.

Explanation:

Given initial speed #u# of car before it enters patch of mud#=24ms^-1#.
Net horizontal resistive force in mud patch#=1.7xx10^4N#

From Newton's Second Law of motion
Net horizontal deceleration #="Resistive Force"/"Mass"#
#:."acceleration "a=-(1.7xx10^4)/1100=-15.bar45ms^-2#

Using the kinematic equation

#v^2-u^2=2as#
where #v# is final velocity, #s# is displacement

Inserting various values we get
#v^2-24^2=2xx(-15.bar45)xx18#
#=>v^2=24^2-556.bar36#
#=>v^2=19.bar63#
#=>v=sqrt(19.bar63)#
#=>v=4.43ms^-1#, rounded to two decimal places.

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