ahh, another calculus problem (INTEGRATION)

[churchdoesmatter]

An object is thrown upward. After 1 second, its velocity is 60 ft per sec. Find its velocity after 4 sec.

Hint: Because of gravity the acceleration of a falling body is 32 ft per sec, if we do not consider air resistance.

 

[aphex]

shouldnt that be a -32 feet per second?

 

[Ladies Man]

no it shouldn't

up is + and down should be negitive

gravity has a -9.8m/s pull on it i believe
but its late... and my brain go no worky

 

[Deeko]

why do you need integration for that? isnt is just -36 ft/s?

 

[ArmenK]

vf=v0+at
vf = 60 +(-32)(3)
vf = -36 ft/s

 

[Logix]

The acceleration due to gravity is -32 ft/sec per second. This means the velocity decreases by 32 ft/s every second. So:

At 1 sec., velocity = 60 ft/s
At 2 sec., velocity = 28 ft/s
At 3 sec., velocity = -4 ft/s
At 4 sec., velocity = -36 ft/s

 

[auyong]

there's no integration in this. v = u + at. We can use 60ft/s as the u and minus 32(3)

 

[vtqanh]

<< v = u + at >>



That equation is obtained by integration:
dv/dt = a
dv = adt
Integrate the left with respect to v, from u (which is the starting velocity) to v (the current velocity)
Integrate the right with respect to t, from 0 to t.
We get:
v - u = at
Thus, v = u +at