Calculate the car's average acceleration

[Sevenheartz]

Homework Statement

A car with a velocity of 25 m/s [E] changes its velocity to 25 m/s in 15s. Calculate the car's average acceleration.

Homework Equations

a = v/t

The Attempt at a Solution

The problem I'm having with this question (And actually, vectors in general) is the direction in the end. I understand how to obtain both the magnitude and angle, but the answer says 2.4 m/s² [45º S of W].

Here's what I have: I drew out the vectors for when the car moves 25 m/s [E] and when it moves 25 m/s , putting the second vector to the tip of the one facing east. If I draw the resultant vector by having it go from the tail of the v_i and to the tip of v_f, I have the right angle triangle that I can solve. But my problem is, the resultant vector is pointing to the east of south, which is clearly wrong. Does the direction change when I find acceleration?

Thank you!

 

[LowlyPion]

Homework Statement

A car with a velocity of 25 m/s [E] changes its velocity to 25 m/s in 15s. Calculate the car's average acceleration.

Homework Equations

a = v/t

The Attempt at a Solution

The problem I'm having with this question (And actually, vectors in general) is the direction in the end. I understand how to obtain both the magnitude and angle, but the answer says 2.4 m/s² [45º S of W].

Here's what I have: I drew out the vectors for when the car moves 25 m/s [E] and when it moves 25 m/s , putting the second vector to the tip of the one facing east. If I draw the resultant vector by having it go from the tail of the v_i and to the tip of v_f, I have the right angle triangle that I can solve. But my problem is, the resultant vector is pointing to the east of south, which is clearly wrong. Does the direction change when I find acceleration?

Thank you!

But the problem says that you started with East Velocity and you ended with South. You went from (15m/s, 0 m/s) TO (0 m/s, 15 m/s).

Your East velocity reversed to get toward South, hence your acceleration was negative East = West and you ended with South of West acceleration to get the result of all 15m/s South.

 

[Sevenheartz]

But the problem says that you started with East Velocity and you ended with South. You went from (15m/s, 0 m/s) TO (0 m/s, 15 m/s).

Your East velocity reversed to get toward South, hence your acceleration was negative East = West and you ended with South of West acceleration to get the result of all 15m/s South.

I think I understand. So if it went from East velocity to North, the direction of the acceleration would be West of North? Also, just to be sure (this is in terms of the question I posted in the beginning)... the resultant vector would have a direction of East of South right?

Thanks for your help.

 

[LowlyPion]

I think I understand. So if it went from East velocity to North, the direction of the acceleration would be West of North? Also, just to be sure (this is in terms of the question I posted in the beginning)... the resultant vector would have a direction of East of South right?

Thanks for your help.

I know it's not easy to wrap your mind around, but it is important in thinking about vectors. The answer vector is described by the answer. It is directed South of West. Not East of South. You would get East of South if you simply added the vectors. But the question they gave you was an initial vector and then the resultant vector. You were asked to find what vector when added to your initial vector would yield the result. That involves a Vector subtraction.

$$\vec{A} + \vec{B} = \vec{C}$$

For instance they gave you A and C and asked you what B was.

$$\vec{B} = \vec{C} - \vec{A} = (-\vec{A}) + \vec{C}$$

For your new example, if you were going East and then instead to North with the same description as given you would end up with a direction North of West or West of North because the angle is 45 degrees.