# Homework Help: Motion in 1 Direction

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1. Sep 25, 2015

### mia_material_x1

1. The problem statement, all variables and given/known data
A particle is moving along the x axis. Its velocity as a function of time is given by v = 5+10t , where v is in
m/s. The position of the particle at t = 0 sec is 20 m. Find
(a) the acceleration as a function of time
(b)the position as a function of time
(c) the velocity of the particle at t = 0 sec.

2. Relevant equations

3. The attempt at a solution
a)
a=dv(t)/dt=10m/s
b)
x(t)=5t +10t^2
c)
V(0)= 5+10*(0s)=5m/s

2. Sep 25, 2015

### Dr. Courtney

3. Sep 25, 2015

### SteamKing

Staff Emeritus
The units of acceleration must be m/s2
When you integrate a function, you must always include the constant of integration, C.

Remember, the position of the particle at t = 0 is x(0) = 20 m

Use this condition to determine C

4. Sep 25, 2015

### mia_material_x1

i am confused if my answer for a) is correct. it asks for acceleration as a function of time, i get 10m/s by computing the derivative of velocity, which does not have t at all

5. Sep 25, 2015

### mia_material_x1

okay thank you very much. needed confirmation.

6. Sep 25, 2015

### mia_material_x1

shouldn't b) be x(t)=5t+5t^2+C because V=5+10t, which is the derivative v=dx/dt ?

7. Sep 25, 2015

### SteamKing

Staff Emeritus
Velocity always has units of time. Velocity is defined as the time rate of change of position. V(t) will be in units of m/s.

When you take the time derivative of something, the units of the something get divided by the units of time.

Also, by definition, an acceleration has units of LT-2, so m/s2 are the correct units.

8. Sep 25, 2015

### SteamKing

Staff Emeritus
Yep. You still use the initial position of the particle to determine the value of C.