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The position of an object moving along a line is given by #p(t) = 4t - sin(( pi )/3t) #. What is the speed of the object at #t = 8 #?

Answer 1

#4.52ms^-1#

Here, we are aware that,

Instantaneous speed=#dx/dt# where "dx" denotes the position of an object at a particular moment (instant) in time and "dt" denotes the time interval.

Now,by using this formula,we have to differentiate the above equation #p(t)=4t-sin(π/3t)# #=>(dp(t))/dt=4(dt/dt)-(dsin(π/3t))/dt# #=>(dp(t))/dt=4-cos(π/3t).(π/3t)##[(dsinx)/dt=cosx]# At t=8,

#=>(dp(t))/dt=4-cos(π/3*8)(π/3) # #=>(dp(t))/dt=4--0.52=4.52#

So the answer will be #4.52ms^-1#

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Answer 2

Isabella Alvarez

The speed of the object at ( t = 8 ) is ( |p'(8)| ), where ( p'(t) ) is the derivative of the position function ( p(t) ) with respect to time. Therefore, calculate ( p'(8) ) and then take its absolute value to find the speed.

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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.