# Kinematics, Displacement from Velocity-Time

• cidilon
In summary, when driving at 75 km/h [North], a fox stops on the road. It takes Andrew 3.4 seconds to stop.
cidilon

## Homework Statement

Andrew is driving his van to deliver groceries in Elmvale. As he travels along Hwy 92, a fox stops on the road. Andrew is traveling at 75 km/h [North] and is 42 m away from the fox when he applies his brakes. It takes him 3.4 s to stop.

a) How far did Andrew travel before stopping?

v1 = -75 km/h [North] or -20.8 m/s [North] (It has to be negative because he is decelerating, right?)
v2 = 0
t = 3.4 s

## Homework Equations

From looking at some examples, i believe i am supposed to use
d = .5(v2-v1)t + v1*t
or if i find acceleration first
d = v1*t + .5*a*t*t

## The Attempt at a Solution

d = .5(v2-v1)t + v1*t
d = .5*(0+20.8)*3.4 - 20.8*3.4
d = -35.36 m [North] or -35 m [North]

As final velocity is known, can i use d = v2*t - .5(v2-v1)t or d = .5(v2+v1)t instead and does it matter?

What i am confused about is that d = .5(v2+v1)t is the area of a trapezoid, where as the slope as i imagine it for this word problem, makes a triangle. How is the area of a trapezoid working for a triangle? Does the slope NOT make a triangle? Should i not visualize this problem?

I really hope that i made myself clear, as it has been bugging me quite a lot!

cidilon said:
v1 = -75 km/h [North] or -20.8 m/s [North] (It has to be negative because he is decelerating, right?)

This is not correct. The sign of acceleration does NOT affect the velocity. The sign of the velocity is only determined by its direction (since it's a vector). If you're going to give the velocity a sign, you'll have to determine which direction is positive (for example, west could be + and east, -) but in this case since there aren't different directions of velocities, that's pointless.

cidilon said:
As final velocity is known, can i use d = v2*t - .5(v2-v1)t or d = .5(v2+v1)t instead and does it matter? !
If both equations are correct, and since acceleration is constant (some equations require constant acceleration), you should be able to use both to determine the distance.

cidilon said:
What i am confused about is that d = .5(v2+v1)t is the area of a trapezoid, where as the slope as i imagine it for this word problem, makes a triangle. How is the area of a trapezoid working for a triangle? Does the slope NOT make a triangle? Should i not visualize this problem?
Distance will not be a slope, it will be an area on a graph just like work would be. It'll be velocity*time on a graph.
Hope this helps!

amy andrews said:

This is not correct. The sign of acceleration does NOT affect the velocity. The sign of the velocity is only determined by its direction (since it's a vector). If you're going to give the velocity a sign, you'll have to determine which direction is positive (for example, west could be + and east, -) but in this case since there aren't different directions of velocities, that's pointless.

I got the idea in an example that i saw earlier. It was a similar problem but acceleration was found first. It went something like this "Kareem was driving his truck at 94 km/h [west]. He starts to apply brakes when he notice the stop sign ahead. It takes him 28 s to come to a complete stop"

For the answer on the other hand they used -94km/h [west] /28s = -0.93m/s2 [west] or 0.93m/s2 [east]. Why was the velocity made negative in this case? I understand that the acceleration needs to be negative because the object is decelerating. Is it okay to make it negative in case of acceleration?

Explain this to me and i think i will be good to go :) hehe

Yep, the acceleration will be negative since the velocity is going down (it's decelerating).

Wonderful, thanks a lot! :)

## 1. What is kinematics?

Kinematics is a branch of physics that deals with the motion of objects without considering the forces that cause the motion.

## 2. How is displacement calculated from velocity-time data?

Displacement can be calculated by multiplying the average velocity by the time interval. This can also be represented by the area under a velocity-time graph.

## 3. What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of how fast and in what direction an object is moving.

## 4. Can an object's displacement be zero even if it has a non-zero velocity?

Yes, an object's displacement can be zero if its velocity is changing in such a way that it returns to its original position. This is known as circular motion.

## 5. What are some common units used for displacement and velocity?

Displacement is commonly measured in meters (m) or kilometers (km), while velocity is measured in meters per second (m/s) or kilometers per hour (km/h).

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