# Motion of an Object: Displacement & Average Velocity

• Stewkatt
In summary, the object travelled a total of 120m in 4.0 seconds, with an average velocity of 12.0m/s.
Stewkatt
New poster has been reminded to always show their work when starting schoolwork threads
Homework Statement
I drew a time line and tried but i think I missed something can someone try this question and show the steps they took? Thank you!
Relevant Equations
Vav=(vf-vi)/2 or delta d/ delta t
a=(vf-vi)/t
An object starts from rest and accelerates at 3.0 m/s2 for 4.0 s. Its velocity remains constant for 7.0 s, and it finally comes to rest with uniform deceleration after another 5.0 s. Find the following:
a. the displacement for each stage of the motion
b. the average velocity over the whole time
interval.

Let us break the question into bite size pieces. First:
An object starts from rest and accelerates at 3.0 m/s2 for 4.0 s.
What is its position at t=4.0s ?
What is its velocity at t= 4.0s ?

Hey, I figured it out. Here is my work.

Delta2 and hutchphd
That's looks correct. Note that you could also have drawn a velocity against time graph and calculated the displacements as the area under each section of the graph.

Steve4Physics and hutchphd
PeroK said:
That's looks correct. Note that you could also have drawn a velocity against time graph and calculated the displacements as the area under each section of the graph.
Hey, my teacher prefers I solve things with algebra with a timeline, but I’ll keep that in mind

hutchphd and PeroK
Stewkatt said:
Hey, my teacher prefers I solve things with algebra with a timeline, but I’ll keep that in mind
Both is best (particularly while you are learning) !

Stewkatt said:
Hey, I figured it out. Here is my work. View attachment 296860
You can make your working a bit shorter.

Stage 2 is at constant velocity (12.0m/s) so using ½(12m/s+12m/s)*7.0s seems a bit excessive.
d₂ = 12.0m/s*7.0s should be acceptable.

For Stage 3. there’s no need to find and use acceleration; just multiply average velocity by time:
##d = \frac {(v_i+v_f)} {2}t##.

PeroK
The quickest way is to note that the maximum speed (during the middle phase) is ##12m/s## and the average speed during both the acceleration and deceleration phases is half of this. So, the displacements are: ##d_1 = 4s \times 6m/s = 24m##, ##d_2 = 7s \times 12m/s = 84m##, ##d_3 = 5s \times 6m/s = 30m##.

Steve4Physics
Thank you for all your help everyone :)

Delta2

## 1. What is displacement?

Displacement is a vector quantity that measures the overall change in position of an object. It is the straight line distance between the object's initial and final positions, and it includes both magnitude and direction.

## 2. How is displacement different from distance?

Distance is a scalar quantity that measures the total path traveled by an object, regardless of its direction. Displacement, on the other hand, takes into account the object's starting and ending points, and the direction it moved in between.

## 3. What is average velocity?

Average velocity is the rate at which an object changes its displacement over a given time interval. It is calculated by dividing the total displacement by the total time taken.

## 4. How is average velocity different from instantaneous velocity?

Average velocity is calculated over a finite time interval, while instantaneous velocity is the velocity of an object at a specific moment in time. Average velocity provides an overall picture of an object's motion, while instantaneous velocity gives information about its motion at a specific point in time.

## 5. Can an object have a non-zero average velocity but a zero displacement?

Yes, an object can have a non-zero average velocity even if its displacement is zero. This can happen if the object moves back and forth between two points, ending up at its initial position. In this case, the total displacement is zero, but the average velocity is non-zero because the object is still moving and changing its position over time.

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