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 #?

Answer 1
#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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Answer 2

To find the speed of the object at ( t = 4 ), you need to calculate the absolute value of the derivative of the position function ( p(t) ) with respect to time ( t ) at ( t = 4 ). So, compute ( |p'(4)| ), where ( p'(t) ) is the derivative of ( p(t) ) with respect to ( t ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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