2d Kinematics Question (Need Answers Checked Please)

[suxatphysix]

Homework Statement

A racecar is speeding around a racetrack with an average speed of 360 km/hr. The racetrack has a turn that changes the direction of the track from east to 30.0 degrees W of N. The racecar completes this turn in 6.54s.

(a) Draw vectors representing the initial and final velocities of the racecar. Use the graphical method to draw the displacement of the racecar as it goes through the turn in the track.

(b) What is the magnitude and direction of the displacement of the racecar as it goes through the turn?

(c) What is the magnitude and direction of the average acceleration of the racecar as it goes through the turn?

Homework Equations

The Attempt at a Solution

converted 360 km/hr to 100m/s

cos30(100m/s)
Vox = 86.60 m/s

sin30(100m/s)
Voy = 50 m/s

$$\Delta$$Rx = 1/2(V1x + Vox)$$\Delta$$t
= 1/2 (86.6m/s)(6.54s)
x= 283.18 m

$$\Delta$$Ry = 1/2(V1y + Voy)$$\Delta$$t
= 1/2(-50m/s)(6.54s)
y = 163.5 m

a = (v1 - v0)/$$\Delta$$t

ax = -150ms / 6.54s = -22.94 m/s$$^{2}$$

ay = 86.6ms / 6.54s = 13.24 ms$$^{2}$$


a = $$\sqrt{(-22.94)^2 + (13.24)^2}$$
a = 26.47 m/s^2

angle = 13.24 / -22.94

angle = -29.985


Hope this is right.

 

[anathema]

Thank you for your post. Your calculations and solution seem to be correct. However, please keep in mind that the direction of the average acceleration should be in the same direction as the change in velocity, which is towards the center of the turn. Therefore, the direction of the average acceleration should be towards the south-west direction, with an angle of -29.985 degrees from the west direction.

Keep up the good work!

 

[m2003]

I appreciate your attempt at solving this problem and using the appropriate equations. However, I would like to point out a few things that could improve your solution.

Firstly, when converting units, it is important to be consistent. In this case, you converted the speed from km/hr to m/s, but you did not do the same for the initial velocity values (V1x and V1y). This could affect the final values of displacement and acceleration.

Secondly, when calculating displacement, it is important to use the correct formula. The formula you used is for average velocity, not displacement. The correct formula for displacement in this case would be: \DeltaR = V0\Deltat + 1/2a\Deltat^2. This would give you a different value for displacement, which would affect the final calculations for acceleration.

Lastly, when calculating the magnitude and direction of acceleration, it is important to use the correct values for V0 and V1. In this case, V0 is the initial velocity (V1x and V1y) and V1 is the final velocity (Vox and Voy). Using the correct values will give you a different angle and magnitude for acceleration.

Overall, your attempt shows a good understanding of the concepts involved in this problem. However, I would recommend double-checking your calculations and being consistent with units to ensure accurate results.