I don't understand how to calculate leg3 for x3? ?

[amyparker30]

I don't understand how to calculate leg3 for x3?

Homework Statement

A rocket sled travels along a straight line. It accelerates at 50m/s2 for 5.0s coasts for 3.0s, then deploys a braking parachute and decelerates at 3.0 m/s2 until coming to a halt. The motion occurs in three different legs.

1. Leg 1:
a. Which type of motion is it?
b. Write the expressions of ?x1 and v1, functions of the time .
c. Calculate ?x1 and v1 at the end of leg 1.

2. Leg 2.
a. Which type of motion is it?
b. Write the expressions of ?x2 and v2 , functions of the time .
c. Calculate ?x2 and v2 at the end of leg 2.

3. Leg 3:
a. Which type of motion is it?
b. Write the expressions of ?x3 and v3, functions of the time.
c. Calculate ?x3 and v3 at the end of leg 3.

4. What is the maximum velocity of the rocket sled?
5. What is the total distance traveled?

Homework Equations

x1 = 1/2a*t^2 v1 = a*t

x2 = v2*t v2 = v1

x3 = 1/2a*t^2 + v*t v3 = a*t + v

The Attempt at a Solution

I just don't know how to get LEG3 x3, i know that v3 is zero because the rocket comes to a halt.

 

[NascentOxygen]

x3 = 1/2a*t^2 + v*t
v3 = a*t + v

Welcome to physics forums.

What are the known variables here, and what is the value for each?

 

[amyparker30]

the values for acceleration and time are given in the question.

i don't know how to calculate x3 using the equations provided?!?

 

[NascentOxygen]

the values for acceleration and time are given in the question.

If that is true, then I was hoping to see your answer. You have the right equations, but just haven't noticed how to use them.

What are the known variables here, and what is the value for each?

 

[amyparker30]

okay for leg 1 my calculations are:

v1=250 m/s
x1=625m

for leg 2 my calculations are:
v2=v1=250m/s
x2=750m

i don't know how to do leg 3 but i know v3=0m/s

 

[I like Serena]

x3 = 1/2a*t^2 + v*t v3 = a*t + v

The Attempt at a Solution

I just don't know how to get LEG3 x3, i know that v3 is zero because the rocket comes to a halt.

Hi amyparker30!

Since you know that v3 is zero, can you use the equation v3 = a*t + v to find the corresponding t?
Afterward you can fill in t in the equation x3 = 1/2a*t^2 + v*t.

 

[amyparker30]

okay so v3 = a*t + v

which is 0= -3(because deceleration) t +250
t=83.3 seconds

using equation (please IS THIS CORRECT)
x3 = 1/2a*t^2 + v*t.
x3= 1/2 (-3) (83.3)^2 + 0
x3= 10408.35m

?

 

[I like Serena]

okay so v3 = a*t + v

which is 0= -3(because deceleration) t +250
t=83.3 seconds

Yep.

using equation (please IS THIS CORRECT)
x3 = 1/2a*t^2 + v*t.
x3= 1/2 (-3) (83.3)^2 + 0
x3= 10408.35m

?

As you can see, your minus sign is off.
In this formula v is your initial speed, which is 250 m/s.
So it should be:
x3= 1/2 (-3) (83.3)^2 + (250) (83.3)

Apparently you've mixed it up with an alternative method, which we'll get to in a moment if you're interested.

 

[amyparker30]

so according to

x3= 1/2 (-3) (83.3)^2 + (250) (83.3) my answer for leg 3 is 10416.6667m?

and therefore What is the total distance traveled? = x1+x2+x3

= 625 + 750 + 10416.67
=11791.67m for total distance travelled?

 

[I like Serena]

Right! :)

 

[amyparker30]

if this is correct,, thank you so much for you help!