# Math Help - Acceleration, Initial Velocity, & Time in the air

1. ## Acceleration, Initial Velocity, & Time in the air

use a(t)=-32 feet per second squared as the acceleration due to gravity. a ball is thrown vertically upward from the ground with an initial velocity of 56 ft/s. for how many seconds will the ball be going upward.

so i know that s''(t)=a(t) and s'(t)=v(t) and that v(0)=56
i also know that integration is used in this problem
i tried it by integrating a(t) first to v(t) and getting -32t+C
using v(0)=56, i know that C=56 and that v(t)=-32t+56
I then integrated v(t) to s(t) and got s(t)=-16t^2 +56t+C and i don't know what to do from there

2. Originally Posted by rawkstar
use a(t)=-32 feet per second squared as the acceleration due to gravity. a ball is thrown vertically upward from the ground with an initial velocity of 56 ft/s. for how many seconds will the ball be going upward.

so i know that s''(t)=a(t) and s'(t)=v(t) and that v(0)=56
i also know that integration is used in this problem
i tried it by integrating a(t) first to v(t) and getting -32t+C
using v(0)=56, i know that C=56 and that v(t)=-32t+56
I then integrated v(t) to s(t) and got s(t)=-16t^2 +56t+C and i don't know what to do from there

s(0) = 0 ... find C for the position function.

3. since s(0)=0 C equals 0 and s(t)=-16t^2+56t then what?

4. All you need to know for this problem is $v(t) = -32t + 56$.

The ball will be going upward as long as $v(t) = -32t + 56 > 0$.

5. i have no idea how that is going to give me the seconds the ball will stay in the air

6. Originally Posted by rawkstar
i have no idea how that is going to give me the seconds the ball will stay in the air
$s(t) = 56t - 16t^2$

set $s(t) = 0$ and solve for $t$

7. t=0 or t=3.5?

8. Originally Posted by rawkstar
t=0 or t=3.5?
Yes, those are the solutions for when the ball is on the ground. This means that the ball is in the air for 3.5 seconds.

9. Originally Posted by rawkstar
t=0 or t=3.5?
which solution makes sense in the context of what the problem asked?

10. Originally Posted by skeeter
which solution makes sense in the context of what the problem asked?
t=3.5

11. Originally Posted by rawkstar
use a(t)=-32 feet per second squared as the acceleration due to gravity. a ball is thrown vertically upward from the ground with an initial velocity of 56 ft/s. for how many seconds will the ball be going upward.
Are you trying to find how long the ball will be in the air or how long the ball will be going upward?