Motion in One Direction: Particle Velocity, Acceleration, and Position

[mia_material_x1]

Homework Statement

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.

Homework Equations

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

 

[Dr. Courtney]

And your question is?

 

[SteamKing]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

a)
a=dv(t)/dt=10m/s

The units of acceleration must be m/s²

b)
x(t)=5t +10t^2

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

c)
V(0)= 5+10*(0s)=5m/s

This answer is correct

 

[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

 

[mia_material_x1]

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 CThis answer is correct

okay thank you very much. needed confirmation.

 

[mia_material_x1]

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 CThis answer is correct

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

 

[SteamKing]

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

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.

 

[SteamKing]

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

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