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How do you find a vehicle's velocity and acceleration in 1 second if an automobile's velocity starting from rest is #v(t)= 90/4t+10# where v is measured in feet per second?

Answer 1

#v=32.5ft//s# #a=32.5ft//s//s#

#v=(90t)/4+10#

If #t=1# #v=(90xx1)/4+10=32.5ft//s#

Acceleration = change in velocity per second. The automobile goes from zero to 32ft/s in 1 second so the acceleration #a=32ft//s//s#

Calculus is not necessary for that; common sense will do.

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Answer 2

Emma Aldridge

To find the vehicle's velocity and acceleration in 1 second:

Substitute t = 1 into the equation v(t) = 90/(4t) + 10 to find the velocity at t = 1 second.
Differentiate the velocity function v(t) with respect to time to find the acceleration function a(t).
Substitute t = 1 into the acceleration function to find the acceleration at t = 1 second.

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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.