Thread: Velocity of a projectile word problem

Heres a word problem i'm having difficulty with.

Velocity of a projectile. The velocity v of a projectile is a linear function of time t that it is in theair. A ball is thrown downward from the top of a tall building. It's velocity is 42 ft per sec after 1 sec and 74 ft per sec after 2 sec. Write v as a linear function of t. What is the velocity when
t = 3.5 seconds?

this problem comes from the linear equation chapter.
i have this to work with
1. v = distance / time
2. t = 3.5 sec
3. m = y2 - y1 / x2 - x1
4. point slope form: y-y1 = m( x-x1 )
5. slope intercept: y = mx+b

but what i have to work with I still dont know how to come up with the soulution can someone please come up w/ the solution. This seems like a good problem to learn for a future physics class that i'll be required to take.

Hmm. Let's see. Any linear function is in the form of , with a non-zero a. Your exercise gave us two pieces of information about the velocity under time (let's call it ), namely:

and


So, replacing x by the appropriate values:

and


Two unknowns, two equations, solve the system and you get the values of a and b, giving you a model that describes the velocity of the object. Then use it to find the velocity at t = 3.5 s