Solving Linear Motion: Car Acceleration

[Cantworkit]

[SOLVED] linear motion

Homework Statement

A car enters a turn at 85 km/h, slows to 55 km/h, and emerges 28 s later at 35 degrees to its original motion, still moving at 55 km/h. What is the magnitude an direction of the average acceleration measure with respect to the car's original direction? Book gives the answer as 0.5 m/s^2 and 142 degrees.

Homework Equations

a=(v2-v1)/delta t

The Attempt at a Solution

V2x= 55 cos 35 degrees=55(.819)=.45 km/h

V1x=80 km/h

a= 35 km/h (1000m)/28s(3600s)= 0.35 m/s^2

I have no idea how to arrive at the direction of the acceleration vector.

 

[lavalamp]

Consider the two speeds you know to be two sides of a triangle, with the third side unknown but opposite an angle of 35 degrees.

From there you can use the law of cosines to work out the third side length, which will be the total change in speed. From that you can also work out the acceleration. You also have enough information to determine the angle of the acceleration relative to the cars initial heading.

Law of cosines:
$$c^{2} = a^{2} + b^{2} - 2*a*b*Cos(C)$$

Oh, and with questions like these, it really helps to draw a diagram.

 

[Moetasim]

I would like to point out that the given answer of 0.5 m/s^2 and 142 degrees may not be entirely accurate. It is important to consider the assumptions and limitations of the problem before arriving at a solution. For example, in this situation, we are assuming that the car is moving in a perfectly circular path, which may not be the case in real life. Additionally, the given answer does not take into account any external forces that may affect the car's motion, such as friction or air resistance.

To accurately solve for the direction of the acceleration vector, we would need more information about the car's motion, such as its velocity at different points during the turn or the radius of the turn. Without this information, it is not possible to determine the direction of the acceleration vector with certainty. As a scientist, it is important to acknowledge the limitations of our calculations and to always consider the uncertainties in our results.