A car starts from rest on a curve with a radius of 150 and accelerates at 1.30 . How many revolutions will the car have gone through when the magnitude of its total acceleration is 3.30 ?
You need to provide units for radious and acceleration. Numbers alone are not enough to define the problem.
When the magnitude of the total acceleration is 3.30 whatevers, the centripetal acceleration is presumably sqrt[3.3^2 - 1.3^2). Use that fact and R to compute V. That and the acceleration will tell you how long it has been on the track. From that, compute the distance travelled and number of revolutions made.
A car starts from rest on a curve with a radius of 150 m and accelerates at 1.00m/s^2 . How many revolutions will the car have gone through when the magnitude of its total acceleration is 2.60m/s^2 ?
To find the number of revolutions the car will have gone through when the magnitude of its total acceleration is 3.30, we can use the centripetal acceleration formula:
a = (v^2) / r
where:
a = centripetal acceleration
v = velocity
r = radius of the curve
Given that the car starts from rest, the initial velocity (v) is 0.
We need to find the final velocity (v) when the magnitude of the total acceleration is 3.30. We can use the following formula to relate acceleration, velocity, and time:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Given that the initial velocity (u) is 0 and the final acceleration (a) is 3.30, we can rewrite the formula as:
v = 0 + (3.30)t
Now, we need to find the time (t) it takes for the car to reach the final velocity.
We can use the following kinematic equation to relate velocity, time, and acceleration:
v = u + at
Since the initial velocity (u) is 0, we can rewrite the equation as:
v = at
Rearranging the formula, we get:
t = v / a
Substituting the values we have, we get:
t = (3.30) / (3.30) = 1 second
Now that we have determined the time it takes for the car to reach the final velocity, we can find the final velocity (v) by substituting the values into the equation:
v = 0 + (3.30)(1) = 3.30 m/s
Now that we know the final velocity of the car (v), we can calculate the centripetal acceleration (a) using the formula:
a = (v^2) / r
Substituting the values we have, we get:
a = (3.30^2) / 150 = 0.0726 m/s^2
To find the number of revolutions the car will have gone through, we need to divide the magnitude of the total acceleration (3.30) by the centripetal acceleration we just calculated (0.0726):
Number of revolutions = |a_total| / |a_centripetal|
Number of revolutions = 3.30 / 0.0726
Number of revolutions = 45.41
Therefore, the car will have gone through approximately 45.41 revolutions when the magnitude of its total acceleration is 3.30.