A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 210 m, and the car completes the turn in 38.0 s.
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors and .
.
The response you submitted has the wrong sign. m/s2 + m/s2
(b) Determine the car's average speed.
. m/s
(c) Determine its average acceleration during the 38.0 s interval.
.
The response you submitted has the wrong sign. m/s2 .
The response you submitted has the wrong sign. m/s2
To solve this problem, we need to break it down into different parts and use the appropriate formulas. Let's start with part (a).
(a) To find the acceleration at point B, we can use the centripetal acceleration formula:
ac = v^2 / r
where ac is the centripetal acceleration, v is the velocity, and r is the radius of the circular path. We can find the velocity using the formula:
v = d / t
where d is the distance travelled (length of arc ABC, 210 m) and t is the time taken (38.0 s).
Substituting the values, we have:
v = 210 m / 38.0 s
Now we can calculate the velocity.
v = 5.526 m/s
The radius of the circular path is not given directly, but we can calculate it using trigonometry.
In the figure, we can see that angle B is given as 35.0°. By drawing a right triangle and applying trigonometry, we can find the radius. Let's call the radius 'r'.
sin(35.0°) = r / 210 m
Solving for r, we get:
r = 210 m * sin(35.0°)
Now we have the radius.
Now we can substitute the values into the centripetal acceleration formula:
ac = (5.526 m/s)^2 / (210 m * sin(35.0°))
Calculating this expression will give us the acceleration at point B.
(b) To find the average speed, we can use the formula:
average speed = total distance / total time
In this case, the total distance is the length of arc ABC (210 m), and the total time is given as 38.0 s.
average speed = 210 m / 38.0 s
Calculating this expression will give us the average speed.
(c) To find the average acceleration during the 38.0 s interval, we can use the formula:
average acceleration = (final velocity - initial velocity) / time interval
In this case, the initial velocity is 0 m/s (since the car starts from rest), and the final velocity can be calculated using the formula:
final velocity = distance / time
The distance travelled is the length of arc ABC (210 m), and the time taken is 38.0 s.
Substituting the values, we have:
final velocity = 210 m / 38.0 s
Now we can calculate the final velocity.
Substituting the initial and final velocities into the average acceleration formula, we have:
average acceleration = (210 m / 38.0 s - 0 m/s) / 38.0 s
Calculating this expression will give us the average acceleration during the 38.0 s interval.