Solving Equation of Motion: Find Acceleration After 4.5 sec

• russjai
In summary: W5lLCBzIGlzIGRvbmUgbm90IHNlZW0gdG8gZ2V0IHRoZSBkaXJlY3RpdmUgb2YgU2luKDIqcGkqdCkgZGV2ZWxvcGVyIGlzIGNvc2kgMi4gUGVmZmVjdCB0aGUgZGlyYWRlZCBvZiBkaXJlY3RpdmUgYWZ0ZXIgNC41IHNlY29uZHMKCkltIGdldHRpbmcgY29uc3VsdGVkIG9uIHdoZXJ
russjai
1. The equation of motion is given by s=sin2πt (m) . Find the acceleration after 4.5 seconds

The Attempt at a Solution

Im getting confused on whether the above equation is for velocity or distance.
I know the derivative of distance is velocity and that the derivative of velocity is acceleration.
If i take the derivative of the above equation i end up with
Sa=cos 2π

This eliminates T , So I am not sure what I am doing wrong.

Cheers

Yes, s is distance. But the derivative d/dt sin(2*pi*t) definitely isn't cos(2*pi). Use the chain rule. What's the derivative of sin(t)? Does the t disappear?

Ok would i be correct in saying the derivative of
S=sin2πt is Sv=2π cos 2πt ?

russjai said:
Ok would i be correct in saying the derivative of
S=sin2πt is Sv=2π cos 2πt ?

Yes, you would.

So to get the derivative of Sv=2π cos 2πt to find acceleration . Would i just use the chain rule again?

If so does this look correct ?
Sa=2π^2 sin 2πt?

thanks

russjai said:
So to get the derivative of Sv=2π cos 2πt to find acceleration . Would i just use the chain rule again?

If so does this look correct ?
Sa=2π^2 sin 2πt?

thanks

Sure, use the chain rule again. But try to do it right. The derivative of cos(t) isn't sin(t), it's -sin(t). And the number in front of the sin(2*pi*t) isn't 2pi^2. Take another try.

ok i still can't seem to get the correct answer. with this equation Sv=2π cos 2πt
Im taking "2π cos " to be the outer function & 2πt to be the inner function

so the derivative of "2π cos" would be just "-sin"
And the derivative of "2πt" would be "2π"

When i put it together i end up with is "-sin 2πt * 2π" or " Sa=-2π sin 2πt

Can you please let me know where I am going wrong. Thanks

(d/dt)[2*pi*cos(2*pi*t)] = (2*pi)*(d/dt) cos(2*pi*t). You really do have to be more careful!

RGV

1. What is the equation of motion?

The equation of motion is a mathematical representation of the relationship between an object's position, velocity, and acceleration over time. It is typically written as d = vit + 1/2at^2, where d is the displacement, vi is the initial velocity, a is the acceleration, and t is the time.

2. How do you find acceleration using the equation of motion?

To find acceleration using the equation of motion, you need to know the initial velocity, final velocity, and time interval. The equation to find acceleration is a = (vf-vi)/t. Plug in the known values and solve for a.

3. What is the significance of the time interval in the equation of motion?

The time interval is the duration of the motion. It is crucial in determining the acceleration because it shows how the velocity changes over time. The shorter the time interval, the more accurate the calculation of acceleration will be.

4. What is the unit of acceleration in the equation of motion?

The unit of acceleration in the equation of motion is meters per second squared (m/s^2). This unit represents the change in velocity over time and is a measure of how quickly an object's speed is changing.

5. Can the equation of motion be used for any type of motion?

No, the equation of motion is specifically for motion with constant acceleration. It cannot be used for motion with varying acceleration, such as in circular motion or freefall. In these cases, different equations and principles, such as Newton's laws of motion, need to be applied.

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