Comparing slopes and accelerations in a graph

[Jahnavi]

Homework Statement

There are two particles A and B moving on x-axis .Their velocities are represented on velocity time (v-t) graph . Graphs of both A and B are straight lines . A makes an angle 120° with the positive x-axis whereas B makes an angle 135° .

1) Slope of A or B is more ?
2) Acceleration of A or B is more ?

Homework Equations

The Attempt at a Solution

This is quite a fundamental problem , but the answer key has left me bit confused .

Slope is given by the tangent of the angle measured anticlockwise .

Tan (120°) = - √3
Tan (135°) = - 1

Tan 135° > Tan 120° , so slope of B is more than slope of A

But acceleration will be given by absolute value of the slopes .Is that correct ?

In that case acceleration of A is more than that of B .The negative sign denotes direction .

So , even though slope of B is more than that of A , acceleration of A is more .

Please let me know if I am thinking incorrectly .

 

[Arman777]

Tan 135° > Tan 120 °, so slope of B is more than slope of A

Not quite like that actually. Think like this If we had $tan(91)=-57$ and $tan(1)=0.017$ which one is more steeper ?

The problem in here is describing the "slope" and "steepness". When we compare the slopes we should think as the steepness of the lines.

But acceleration will be given by the absolute value of the slopes.Is that correct?

Without saying acceleration "magnitude" it doesn't sound right, since it's a vector quantity.

As you said negative sign represents that the acceleration is in the negative direction of the velocity.

 

[Jahnavi]

Isn't definition of slope of a line - tangent of the angle made by the line with the positive x- axis ?

By this definition , isn't slope of B greater than A ?

 

[Arman777]

Slope is a different quantity than numbers. For example -1>-3 yes but we are defining these numbers for a slope.
m=-3 and -3 are not the same thing.

 

[Jahnavi]

Slope is a different quantity than numbers. For example -1>-3 yes but we are defining these numbers for a slope.
m=-3 and -3 are not the same thing.

Are you saying that while comparing slopes of two lines , we should compare absolute value of the slopes ( irrespective of their signs ) ?

 

[Arman777]

Are you saying that while comparing slopes of two lines , we should compare absolute value of the slopes ( irrespective of their signs ) ?

Yes exactly.