A car drives around a curve with radius 150 m at a speed of 30 m/s. What is the average acceleration at? a) 180 degrees. b) 60 degrees around the curve ?
Given answers are:3.8 m/s2 and 5.7 m/s2
Help please :))
To find the average acceleration at a particular point on the curve, we need to calculate the centripetal acceleration. The centripetal acceleration is given by the formula:
a = v^2 / r
where "v" is the velocity and "r" is the radius of the curve.
a) To find the average acceleration at 180 degrees, we need to calculate the velocity at that point. At 180 degrees, the car has completed half of the curve, so it has traveled a distance equal to half the circumference of the circle with a radius of 150 m.
Circumference = 2 * π * r
= 2 * 3.14159 * 150 m
≈ 942.478 m
Therefore, the distance traveled at 180 degrees = half of the circumference = 942.478 m / 2 = 471.239 m.
To find the time taken to travel this distance, we can use the formula:
distance = velocity * time
Rearranging the formula, we get:
time = distance / velocity
time = 471.239 m / 30 m/s
≈ 15.708 s
Next, we can calculate the average acceleration using the centripetal acceleration formula:
a = v^2 / r
= (30 m/s)^2 / 150 m
= 900 m^2/s^2 / 150 m
≈ 6 m/s^2
Therefore, the average acceleration at 180 degrees is approximately 6 m/s^2.
b) To find the average acceleration at 60 degrees around the curve, we can follow a similar process.
To find the distance traveled at 60 degrees, we need to find the fraction of the circumference covered by 60 degrees. Since there are 360 degrees in a circle, the fraction is:
fraction = 60 degrees / 360 degrees
= 1/6
Therefore, the distance traveled at 60 degrees = fraction of the circumference = (1/6) * 942.478 m ≈ 157.080 m.
Again, we need to find the time taken to travel this distance:
time = distance / velocity
= 157.080 m / 30 m/s
≈ 5.236 s
Finally, we can calculate the average acceleration:
a = v^2 / r
= (30 m/s)^2 / 150 m
= 900 m^2/s^2 / 150 m
≈ 6 m/s^2
Therefore, the average acceleration at 60 degrees is approximately 6 m/s^2.
It seems like there may be a mistake in the given answers. The correct answers based on the calculations are both approximately 6 m/s^2, not 3.8 m/s^2 and 5.7 m/s^2.
To determine the average acceleration at a given point on a curve, you can use the centripetal acceleration formula. Centripetal acceleration is the acceleration experienced by an object moving in a curved path due to the change in direction.
The formula for centripetal acceleration is given as:
a = v^2 / r
Where:
- a is the centripetal acceleration
- v is the velocity of the object
- r is the radius of the curve
Now, let's calculate the average acceleration at each of the given points:
a) At 180 degrees:
To calculate the average acceleration at 180 degrees, we need to know the change in velocity at that point. Without that information, we cannot calculate the acceleration accurately.
b) At 60 degrees:
Given:
- Radius of the curve (r) = 150 m
- Speed of the car (v) = 30 m/s
Using the centripetal acceleration formula:
a = v^2 / r
a = (30 m/s)^2 / 150 m
a = 900 m^2/s^2 / 150 m
a = 6 m/s^2
So, the average acceleration at 60 degrees around the curve is 6 m/s^2.
It seems that the given answer for the average acceleration at 60 degrees is 5.7 m/s^2, which is slightly different from the calculation. This discrepancy may be due to rounding errors or slight variations in the given values.