The speed of a point on a rotating turntable, which is 0.264 m from the center, changes at a constant rate from rest to 0.902 m/s in 1.94 s.

At t1 = 0.64 s, find the magnitude of the tangential acceleration.
Answer in units of m/s2

I assumed the velocity was constant so i divided .902/the time .64 to get acceleration at that time =1.41m/s^2 but this was incorrect...what am i doing wrong???

Well, it seems like you're close, but not quite there! Let's take a closer look.

First, let's clarify that the velocity is not constant since it changes from rest to 0.902 m/s in 1.94 s. This means we need to consider the acceleration of the point.

To find the magnitude of the tangential acceleration at t1 = 0.64 s, we can use the following formula:

acceleration = (change in velocity) / (change in time)

So, to calculate the change in velocity, we subtract the initial velocity (which is 0 since it starts from rest) from the final velocity (0.902 m/s):

change in velocity = 0.902 m/s - 0 m/s = 0.902 m/s

Next, we calculate the change in time, which is given as t1 = 0.64 s:

change in time = t1 - 0 s = 0.64 s - 0 s = 0.64 s

Now, we can plug these values into the acceleration formula:

acceleration = (0.902 m/s) / (0.64 s) = 1.41 m/s^2

So, the magnitude of the tangential acceleration at t1 = 0.64 s is 1.41 m/s^2.

Looks like you had the right idea but just made a small mistake in your calculations. Keep up the good work and don't let those pesky calculations clown around with your answers!

Your approach was correct in terms of finding the average acceleration by dividing the change in velocity by the change in time. However, since the speed of the point on the rotating turntable changes at a constant rate, it implies that the acceleration is not constant. Therefore, you need to find the instantaneous acceleration at t1 = 0.64 s by finding the derivative of the speed with respect to time.

To find the magnitude of the tangential acceleration, you can use the formula:
a = (dv/dt)

Given that the speed changes from rest to 0.902 m/s in 1.94 s, you can find the constant rate of change by dividing the change in speed by the change in time:
a = (0.902 m/s - 0 m/s) / (1.94 s - 0 s)
a = 0.902 m/s / 1.94 s
a ≈ 0.465 m/s²

Now, to find the magnitude of the tangential acceleration at t1 = 0.64 s, you need to substitute the time into the acceleration formula:
a = (dv/dt) = a₀ + (α₀)t
where a₀ is the initial velocity and α₀ is the constant rate of change of acceleration.

Since the initial velocity is 0 m/s (rest) and the constant rate of change of acceleration is 0.465 m/s², you can substitute the values:
a = 0 m/s + (0.465 m/s²)(0.64 s)
a ≈ 0.298 m/s²

Therefore, the magnitude of the tangential acceleration at t1 = 0.64 s is approximately 0.298 m/s².

To find the magnitude of the tangential acceleration at time t1 = 0.64 s, you cannot assume that the velocity is constant. The problem states that the point on the rotating turntable starts from rest and changes its speed at a constant rate.

To find the tangential acceleration, you can use the formula:
acceleration = (final velocity - initial velocity) / time

However, since we don't have the initial velocity, we need to find it first.

Let's use the equation of motion to find the initial velocity:
final velocity = initial velocity + acceleration * time

Given:
- final velocity (v) = 0.902 m/s
- time (t) = 1.94 s

Rearranging the equation, we have:
initial velocity = final velocity - acceleration * time

Substituting the given values, we get:
initial velocity = 0.902 m/s - acceleration * 1.94 s

Now, we can substitute the calculated initial velocity back into the equation to find the acceleration at time t1 = 0.64 s:
acceleration = (0.902 m/s - initial velocity) / 1.94 s

To find the initial velocity, we need to use the position of the point on the turntable at t1 = 0.64 s.

The distance from the center of the turntable is given as 0.264 m. This distance is the same as the radius of the turntable. The formula to calculate linear velocity is:
linear velocity = angular velocity * radius

We can rearrange this equation to find the angular velocity:
angular velocity = linear velocity / radius

The angular velocity represents how fast the turntable is rotating.

Substituting the given values, we have:
angular velocity = initial velocity / 0.264 m

Now, let's calculate the initial velocity using the angular velocity:
initial velocity = angular velocity * 0.264 m

Now that we know how to find the initial velocity at t1 = 0.64 s, let's solve for the magnitude of the tangential acceleration:

1. Calculate the angular velocity using the angular velocity formula: angular velocity = initial velocity / 0.264 m
2. Calculate the initial velocity using the equation: initial velocity = angular velocity * 0.264 m
3. Calculate the final velocity using the equation: final velocity = initial velocity + acceleration * time
4. Rearrange the equation to solve for the acceleration: acceleration = (final velocity - initial velocity) / time
5. Substitute the values into the equation and solve for the magnitude of the tangential acceleration at t1 = 0.64 s.

By following these steps, you will be able to accurately calculate the magnitude of the tangential acceleration at t1 = 0.64 s.