# Kinematics and acceleration problem

• aaronfue
In summary: I was so close!In summary, the particle moved along a straight line such that its acceleration was a = (4t2-2) \frac{m}{s^2}, where t is in seconds. When t = 0, the particle is located 1 m to the left of the origin, and when t = 2 s, it is 20 m to the left of the origin. When t = 4.3s, the particle is located 52.16 m to the left of the origin.
aaronfue

## Homework Statement

A particle moves along a straight line such that its acceleration is a = (4t2-2) $\frac{m}{s^2}$, where t is in seconds. When t = 0, the particle is located 1 m to the left of the origin, and when t = 2 s, it is 20 m to the left of the origin. Determine the position of the particle when t = 4.3s.

2. Homework Equations & The attempt at a solution.

I am just stuck on this. I know I should already know how to do this but right now my mind is blank!
I know that I can get the velocity equation by integrating, but when I try to use t=2 s, and then using the equation x=xo+vot+$\frac{1}{2}$at2, I am not even close to the x=20.

The kinematics equation you mention is good only for constant acceleration, but the acceleration in the problem varies with time, so you have to go back to basics. Start with the definition of acceleration: $a = dv/dt$.

aaronfue said:
x=xo+vot+$\frac{1}{2}$at2
That equation is only valid for constant acceleration.

What do you get when you integrate the acceleration equation?

haruspex said:
That equation is only valid for constant acceleration.

What do you get when you integrate the acceleration equation?

After I integrate the acceleration, I get:

v(t)= ($\frac{4}{3}$t3 - 2t) $\frac{m}{s}$

aaronfue said:
After I integrate the acceleration, I get:

v(t)= ($\frac{4}{3}$t3 - 2t) $\frac{m}{s}$

Don't forget the constant of integration.
Then get the equation for distance as a function of time.

Don't forget the constant of integration.

Then the next step is to find the displacement.

tms said:
Don't forget the constant of integration.

Then the next step is to find the displacement.

s(t) = $\frac{t^4}{3}$ - t2 + c1t + c2

c1 is the constant after integrating for v(t) & c2 is the constant for s(t).

Do I have to set the constants equal to the given positions and t=0 and t=2?

aaronfue said:
Do I have to set the constants equal to the given positions and t=0 and t=2?
No. You plug in the value for $t$, and then solve for the constants.

tms said:
No. You plug in the value for $t$, and then solve for the constants.

Ok. I plugged in the t=0, s=1 and got c2 = 1 (I think this would be -1 since the location is to the left of the origin?)

So I then plugged t=2, s= -20 and my c1 = -9.84

Finally I plugged my c1 and c2 into my s(t) equation:

s(t) = $\frac{1}{3}$t4 - t2 - 9.84t -1

And after using t=4.3, I got s = 52.16 m

Unfortunately, this is not correct. The correct answer was 50.8 m. I'm not sure where I messed up, but I'm thinking it was my rounding.

Last edited:
aaronfue said:
Ok. I plugged in the t=0, s=1 and got c2 = 1 (I think this would be -1 since the location is to the left of the origin?)

So I then plugged t=2, s= -20 and my c1 = -9.84

Finally I plugged my c1 and c2 into my s(t) equation:

s(t) = $\frac{1}{3}$t4 - t2 - 9.84t -1

And after using t=4.3, I got s = 52.16 m

Unfortunately, this is not correct. The correct answer was 50.8 m. I'm not sure where I messed up, but I'm thinking it was my rounding.
Found my mistake! I was subtracting my numbers from +20 and not using -20 when calculating my c1!

I got:
s = 50.75 = 50.8 m!

Dang!

## What is kinematics?

Kinematics is the study of motion, including the concepts of displacement, velocity, and acceleration.

## What is acceleration?

Acceleration is the rate of change of velocity over time. It can be calculated by dividing the change in velocity by the change in time.

## How is acceleration related to velocity?

Acceleration and velocity are related by the equation a = Δv/Δt, where a is acceleration, Δv is the change in velocity, and Δt is the change in time.

## What are some common units of acceleration?

The most commonly used units of acceleration are meters per second squared (m/s^2) and kilometers per hour squared (km/h^2).

## How do you solve a kinematics and acceleration problem?

To solve a kinematics and acceleration problem, you must first identify the known and unknown variables, and then use the appropriate equations, such as the kinematic equations, to solve for the unknown variable.

### Similar threads

• Introductory Physics Homework Help
Replies
5
Views
266
• Introductory Physics Homework Help
Replies
22
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
579
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
18
Views
402
• Introductory Physics Homework Help
Replies
4
Views
912
• Introductory Physics Homework Help
Replies
10
Views
874
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
4K