# Solving Linear Motion: Car Acceleration

• Cantworkit
In summary, the problem involves a car entering a turn at 85 km/h, slowing down to 55 km/h, and exiting the turn 28 seconds later at a 35 degree angle to its original direction, still moving at 55 km/h. The average acceleration with respect to the car's original direction is 0.5 m/s^2 at an angle of 142 degrees. To solve this problem, we can use the equation a=(v2-v1)/delta t and the law of cosines to determine the magnitude and direction of the acceleration vector. It is also helpful to draw a diagram to visualize the problem.
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.

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.

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.

## 1. What is linear motion?

Linear motion is a type of motion in which an object moves along a straight line with a constant velocity or acceleration.

## 2. How is car acceleration calculated?

Car acceleration is calculated by dividing the change in velocity by the change in time. This can be represented by the formula a = (vf - vi) / t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the change in time.

## 3. What are the units of car acceleration?

The unit of car acceleration is meters per second squared (m/s²) in the metric system or feet per second squared (ft/s²) in the imperial system.

## 4. How does car acceleration affect driving?

Car acceleration affects the speed and movement of a vehicle. A higher acceleration can result in a faster speed and quicker movement, while a lower acceleration can result in a slower speed and gradual movement.

## 5. What factors can affect car acceleration?

Some factors that can affect car acceleration include the engine power, weight of the car, friction of the road, and aerodynamics of the car. Other external factors such as weather conditions and road conditions can also impact car acceleration.

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