<u>ANSWER:
</u>
If a ball is thrown into the air with a velocity of 34 feet per second, then velocity of the ball after 1 second is 2 feet per second
<u>SOLUTION:
</u>
Given, a ball is thrown into the air with a velocity of 34 feet per second
Initial velocity (u) = 34 feet per second
And also given a relation between displacement and time =
--- eqn 1
We need to find the velocity when t = 1 ; v = ?
We know that, v = u + at and ![\mathrm{s}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^{2}](https://tex.z-dn.net/?f=%5Cmathrm%7Bs%7D%3D%5Cmathrm%7But%7D%2B%5Cfrac%7B1%7D%7B2%7D%20%5Cmathrm%7Bat%7D%5E%7B2%7D)
where v is instantaneous velocity and u is initial velocity
a is acceleration
t is time interval
s is displacement
using the displacement and time relation eqn (1) we get
Now, when t = 1, displacement s = 34(1) – 16(1)
![\mathrm{ut}+\frac{1}{2} \mathrm{at}^{2}=34-16](https://tex.z-dn.net/?f=%5Cmathrm%7But%7D%2B%5Cfrac%7B1%7D%7B2%7D%20%5Cmathrm%7Bat%7D%5E%7B2%7D%3D34-16)
![34 \times 1+\frac{1}{2} \times a \times 1^{2}=18](https://tex.z-dn.net/?f=34%20%5Ctimes%201%2B%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20a%20%5Ctimes%201%5E%7B2%7D%3D18)
![34+\frac{a}{2}=18](https://tex.z-dn.net/?f=34%2B%5Cfrac%7Ba%7D%7B2%7D%3D18)
![\begin{array}{l}{\frac{a}{2}=18-34} \\\\ {\frac{a}{2}=-16} \\ {a=-16 \times 2} \\ {a=-32}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Cfrac%7Ba%7D%7B2%7D%3D18-34%7D%20%5C%5C%5C%5C%20%7B%5Cfrac%7Ba%7D%7B2%7D%3D-16%7D%20%5C%5C%20%7Ba%3D-16%20%5Ctimes%202%7D%20%5C%5C%20%7Ba%3D-32%7D%5Cend%7Barray%7D)
here, -ve sign indicates that object is in deceleration . so acceleration is -32 ft/s
now put a value in v = u + at
v = 34 + (-32)(1)
v = 34 – 32
v = 2 ft/s
Hence, velocity of the ball after 1 second is 2 ft/s