I please need your help with the following homework problems. I want to make sure that I followed the correct procedure in solving these problems. Thanks!
1. Solve the Initial Value Problem:
a) dy/dx= (x)^1/2, y(4)= 0
b) dy/dx= cos 2x, y(0)= 1
c) dy/dx= xe^(-x), y(0)=1
2. A moving particle has acceleration a(t)=5, intial velocity v=1, and initial position x=2. Find the position function x(t) of the particle.
3. A moving particle has acceleration a(t)= 2t+1, initial velocity v=-7, and initial position x=4. Find the position function x(t) of the particle.
4. The skid marks made by an automoblie indicated that its brakes were fully applied for a distance of 75m before it came to a stop. The car in quesion is known to have a constant deceleration of 20 m/s^2 under these conditions. How fast - in km/h - was the car traveling when the brakes were first applied?
i will only do 2, since 3 is similar
2.
You should have some background knowledge here. You are expected to know that.
(we usually use s, but since you use x, i will also)
if x(t) = position function
v(t) = x'(t) = velocity function
a(t) = v'(t) = acceleration function
So we have:
we are told that (that is, when t = 0, v = 1):
Thus
we are told that (that is, when t = 0, x = 2):
You could also use SUVAT equations to answer these questions, but i figured this was the method you were after. The SUVAT equations were derived from similar procedures I would think
use SUVAT equations for this
Let be displacement
Let be initial velocity
Let be final velocity
Let be acceleration
Let be time
Our knowns are:
m/s^2
m
m/s
Remember to watch your units, you can work in meters and seconds and convert at the end, or convert and work in the right units from the beginning
Use to solve for
And that's it