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???
To find the magnitude of the tangential acceleration at t1 = 0.64 s, you cannot assume that the velocity is constant. Instead, you need to calculate the average tangential acceleration over the given time interval.
The average tangential acceleration can be found using the formula:
Average tangential acceleration = (change in velocity) / (change in time)
First, calculate the change in velocity:
Velocity at t2 = 0.902 m/s
Velocity at t1 = 0 m/s (rest)
Change in velocity = Velocity at t2 - Velocity at t1
Change in velocity = 0.902 m/s - 0 m/s
Change in velocity = 0.902 m/s
Next, calculate the change in time:
Time at t2 = 1.94 s
Time at t1 = 0.64 s
Change in time = Time at t2 - Time at t1
Change in time = 1.94 s - 0.64 s
Change in time = 1.30 s
Now, calculate the average tangential acceleration:
Average tangential acceleration = (change in velocity) / (change in time)
Average tangential acceleration = 0.902 m/s / 1.30 s
Average tangential acceleration ≈ 0.6938 m/s^2
Therefore, the magnitude of the tangential acceleration at t1 = 0.64 s is approximately 0.6938 m/s^2.