The position of an object moving along a line is given by p(t) = t - 3sin(( pi )/3t) . What is the speed of the object at t = 4 ?

1 Answer
Gregorio Manea
Nov 26, 2017

p(t)=t-3sin(pi/3t)
t=0 => p(0)=0m
t=4 => p(4)=4-3sin(pi/3*4)=>
p(4)=4-3sin(pi+pi/3) (1)
sin(pi+t)=-sin(t) (2)
(1)+(2)=>p(4)=4-(3*(-)sin(pi/3))=>
p(4)=4+3*sqrt(3)/2
p(4)=(8+3sqrt(3))/2m

Now it depends on the extra information given:

1.If the acceleration isn't constant:
Using the law of space for the varied linear uniform movement:
d=V""_0*t+(a*t^2)/2
where
d is the distance,V""_0 is the initial speed,a is the acceleration and t is the time when the object is in position d.

p(4)-p(0)=d
Assuming that the initial speed of the object is 0m/s
(8+3sqrt(3))/2=0*4+(a*16)/2=>
a=(8+3sqrt(3))/16m/s^2

Finally the speed of the object at t=4 is
V=a*4=(8+3sqrt(3))/4m/s

2.If the acceleration is constant:
With the law of linear uniform movement:
p(4)=p(0)+V(t-t""_0)
You will get:
(8+3sqrt(3))/2=0+V*4=>
V=(8+3sqrt(3))/8m/s

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