Two Physics Question About Linear Motion I'm Stuck On

Question

Hello! I was going through my review questions and I got eight out of the ten questions done, but no matter what I do, I can't seem to figure out these two questions. Any help given would be highly appreciated! 

1.)  On your way to the grocery store though there is some slow driving person in front of you so you slam on the gas going from 30. mi/hr to 60. mi/hr. Luckily your husband brought a stop watch and told you the whole thing took place in 10.s. What is your acceleration and how far did you go? 

2.)  Two spacecraft are 13,500 m apart and moving directly toward each other. Spacecraft#1has velocity 525 m/s and accelerates at a constant -15.5 m/s2. They want to dock, which means they have to arrive at the same position at the same time with zero velocity. 

(a) What should the initial velocity of the spacecraft#2 be?

(b) What should be #2 constant acceleration?

Answer 1

1)  acceleration a = Δv / Δt = (60-30)/[10 sec] but you must convert 10 seconds to hours units: 10/3600.  Simplify a.

 

distance = vt + ½(at²) can be used to calculate the time covered during this 10 seconds of passing the slow driver.

 

Answer 2

I will set these up for you and you do the math.

 

(1)

 

a = (v₂ - v₁)/t 

 

v₂ = 60 mi/hr

v₁ = 30 mi/hr

t = 10 sec = 10/3600 hrs

 

Decide whether you want the acceleration in mi/s² or mi/hr², and plug in the numbers to get a.

 

From kinematics,

 

v₂² - v₁² = 2ad ⇒

 

d = (v₂² - v₁²) / (2a)

 

Plug in the numbers in appropriate units and get the distance d.

 

(2)

 

Find how long it takes spacecraft 1 to stop, and how far it has traveled.

 

d = initial separation distance = 13500 m

 

v₁(t) = v_1i + a₁t = 525 - 15.5t

 

Set v₁(t) = 0 and solve for t.

 

525 - 15.5t = 0

 

Solve for t.  That is how long it takes to come to instantaneous rest.  Its travel distance is

 

x₁ = v_1it + (1/2)a₁t² = 525t - (15.5/2)t²

 

Plug in the travel time t computed above, and get the travel distance x₁.  Now use these results to calculate initial speed and acceleration of spacecraft 2.  It travels for the same length of time as 1, so use the same t you calculated above.

 

v₂(t) = v_2i + a₂t

 

Set v₂(t) = 0

 

(i)  v_2i + a₂t = 0

 

You know t, but you have 2 unknowns v_2i and a₂, so you need a second equation.  The distance that 2 travels gives you the second equation.

 

x₂ = d - x₁

 

x₁ = distance traveled by 1, which you calculated above, and you know d.

 

(ii)  d - x₁ = v_2it + (1/2)a₂t²

 

Plug d, x₁, and t into equations (i) and (ii) and solve for the unknwons v_2i and a₂.  You have a system of 2 linear equations in 2 unknowns, which you should know how to solve.  There will be a lot of number crunching!