Antiderivative word prob: What constant acceleration is requ

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sofiaahmed

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What constant acceleration is required to increase the speed of a car from 30 mi/r to 50 mi/h in 5 seconds?

I am supposed to use antiderivative. Please help me figure out how to do this. Thanks in advance.
 
You are given that v(0) = 30 and v(5) = 50.

You are given that acceleration is some constant, so a(t) = c for some constant value "c".

You know that "velocity" is the antiderivative of "acceleration".

Antidifferentiate the "acceleration" function, and use the given data points to find the exact form of the "velocity" function.

If you get stuck, please reply showing how far you have gotten in working through these steps. Thank you.

Eliz.
 
you do not need calculus to do this, just the definition of average acceleration ...

\(\displaystyle \L a = \frac{\Delta v}{\Delta t}\)

since the given time is in seconds, I would convert the given speeds from miles/hr to ft/sec.
 
d^2x/dt^2=k integrate
dx/dt = kt+c

given :
at t=0 dx/dt=30
at t=5 dx/dt=50

find k the constant acceleration
substitute t=0 dx/dt=30
30=k0+c
c=30

dx/dt=kt+30
at t=5 dx/dt=50 substitute
50=k5+30
k=4mph/sec you can change units if you wish
Arthur
 
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