How to calculate instantaneous acceleration?

In summary, the instantaneous acceleration can be found by calculating the slope of the velocity-time graph. In the given graph, the slope during the time interval of 30s to 40s is a straight line, indicating uniform acceleration. Therefore, the instantaneous acceleration at t = 35s is -1.667 m/s^2, which is also the slope of the tangent line at that point.
  • #1
treyh
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This is the graph and question:
http://img193.imageshack.us/img193/3489/physicquestion.jpg [Broken]

I cannot seem to find the instantaneous acceleration. I must be doing it wrong because I'm pretty sure to find the the inst. acceleration all i need to know is the tangent line equation.

I've tried a bunch of answers but can't seem to get it right. I need to express the answer in m/s^2 and not km/h but that is easy to convert.

I haven't had much physics experience. How do i find the instantaneous acceleration?

Thanks
 
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Since the acceleration is uniform, instantaneous acceleration = average acceleration.

acceleration = slope of v-t graph

from the graph, the slope of the graph during time = 30s to 40s is a straight line (that means the slope is not varying), that means the acceleration uniform.

so the instantaneous acceleration at time = 35s :
= [(60/3.6) - 0 / (30 - 40)] = -1.667 m/s^2.
 
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treyh said:
I'm pretty sure to find the the inst. acceleration at t = 35 seconds all i need to know is the tangent line equation.
That's correct, so what is the definition of instantaneous acceleration and what is the slope of that line at t = 35 s?
 

What is instantaneous acceleration?

Instantaneous acceleration is the rate of change of an object's velocity at a specific moment in time. It is often denoted as "a" and measured in meters per second squared (m/s^2).

How do you calculate instantaneous acceleration?

To calculate instantaneous acceleration, you need to know the change in velocity (Δv) and the change in time (Δt) at a specific moment. The formula for instantaneous acceleration is a = Δv/Δt. This can also be written as a = (v2 - v1)/(t2 - t1), where v2 and v1 are the final and initial velocities, and t2 and t1 are the final and initial times.

Is instantaneous acceleration the same as average acceleration?

No, instantaneous acceleration and average acceleration are not the same. Average acceleration is the change in velocity over a period of time, while instantaneous acceleration is the change in velocity at a specific moment in time.

What is the difference between instantaneous acceleration and instantaneous speed?

Instantaneous acceleration and instantaneous speed are two different concepts. Instantaneous acceleration is the rate of change of velocity, while instantaneous speed is the magnitude of the velocity at a specific moment in time. In other words, instantaneous acceleration tells us how fast an object's velocity is changing, while instantaneous speed tells us how fast the object is moving at that moment.

Can instantaneous acceleration be negative?

Yes, instantaneous acceleration can be negative. This means that the object is slowing down or changing direction at a specific moment in time. It is important to note that the sign of the acceleration does not indicate the direction of motion, but rather the direction of the change in velocity.

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