Are my calculations correct a=dv/dt question (Find a = dv/dt, given v=2000−14t−0.006t^4 m/s)

[boltonr100]

Good morning all,

new to this and struggling a little with this topic. Ive tried to answer thre following question...

Q) Find the acceleration a=dv/dt of an object falling through the atmosphere with a velocity of: v=2000−14t−0.006t^4 m/s..... Give the acceleration after t=3s

A) taken 2000-14t-0.006t^4 and differentiated it to v = -14 -0.024t^3 then inputted t=3 to give my answer of a = -14.648?

Any advice would be appreciated... this seems to be a subject im failing on, and hoping being able to do this might allow me to complete the rest of my question set.

Thanks in advance

Richard

 

[R.M.]

Looks good. The only other thing I would include would be the units: m/s².

 

[Steven G]

v=2000−14t−0.006t^4 m/s..... Give the acceleration after t=3s

A) taken 2000-14t-0.006t^4 and differentiated it to v = -14 -0.024t^3

You have two definitions of v and they are different!. The one should have a instead of v.

 

[alyh]

For this topic overall, knowing that a=v'=x'' helped me a lot (acceleration=derivative of velocity=second derivative of displacement).
This applies for integration too, just in the opposite direction, if that makes sense. The integral of a is v, the double integral of a is x, the integral of v is x, and so on.

This graphic (from https://www.statisticshowto.com/calculus-problem-solving/acceleration-find-average-instantaneous/) sums it up well:


I hope this helps!