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

In summary: So, x(0) = 20 = C.In summary, the particle is moving along the x axis with a velocity of v = 5+10t m/s. The acceleration as a function of time is a = 10 m/s2. The position of the particle at time t is x(t) = 5t + 5t^2 + 20 m. The velocity of the particle at t = 0 sec is 5 m/s.
  • #1
mia_material_x1
22
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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
 
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  • #3
mia_material_x1 said:

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
 
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  • #4
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
SteamKing said:
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.
 
  • #6
SteamKing said:
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 ?
 
  • #7
mia_material_x1 said:
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.
 
  • #8
mia_material_x1 said:
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.
 

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

What is motion in 1 direction?

Motion in 1 direction refers to the movement of an object along a straight path or in a straight line.

What are the key principles of motion in 1 direction?

The key principles of motion in 1 direction include velocity, acceleration, and displacement. Velocity is the rate of change of an object's position, while acceleration is the rate of change of an object's velocity. Displacement is the distance and direction an object has moved from its starting point.

How is motion in 1 direction measured?

Motion in 1 direction is measured using units of distance, such as meters or kilometers, and units of time, such as seconds or minutes. These measurements are used to calculate velocity, acceleration, and displacement.

What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of how fast an object is moving in a specific direction. Therefore, velocity takes into account both the speed and direction of an object's motion.

How does constant acceleration affect motion in 1 direction?

Constant acceleration means that an object is changing its velocity at a constant rate. This can cause the object to either speed up or slow down, depending on the direction of its acceleration. As a result, the object's displacement will also change at a constant rate.

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