Find the total time taken and acceleration in the given problem-Kinematics

In summary: But then you said a=10/3=3 1/3 m/s^2. In summary, the conversation involves solving a problem involving a velocity-time graph with three parts: a, c, and d. The equations and values for each part are provided, but there seems to be a math error in part d where the value for acceleration does not match the given equation. The original thread title promised a graph, but the user is more interested in solving the highlighted parts of the problem.
  • #1
chwala
Gold Member
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Homework Statement
Kindly see attached; interest only on parts;

a, c and d
Relevant Equations
Kinematics equations
This is the question; I made some math error...then i just realised this is an easy problem...anyway, i know you guys may have an alternative approach to this; kindly share...

1675764481515.png
For part (a) i have;

##a=\dfrac{10}{t_1}## and ##2a=\dfrac{20-10}{(t_1+t_2)-t_1}##

##⇒\dfrac{10}{t_1}=\dfrac{10}{2t_2}##

##t_1=2t_2##

For part (c); i have

##A_{total}= A_1+A_2+A_3##

where

##A_1=\dfrac{1}{2} × t_1 × 10##

##A_2=\dfrac{1}{2} × t_2 × (20+10)##

##A_3= 24 × 20##

##555=10t_2+15t_2+480##

##75=25t_2##

##t_2=3## seconds

##t_{total}=6+3+24=33##seconds

For part (d),

##a=\dfrac{10}{3}=3\frac{1}{3} m/s^2##

Cheers! Bingo!
 
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  • #2
chwala said:
Homework Statement:: Kindly see attached; interest only on parts;

a, c and d
Relevant Equations:: Kinematics equations

This is the question; I made some math error...then i just realised this is an easy problem...anyway, i know you guys may have an alternative approach to this; kindly share...

View attachment 321883For part (a) i have;

##a=\dfrac{10}{t_1}## and ##2a=\dfrac{20-10}{(t_1+t_2)-t_1}##

##⇒\dfrac{10}{t_1}=\dfrac{10}{2t_2}##

##t_1=2t_2##

For part (c); i have

##A_{total}= A_1+A_2+A_3##

where

##A_1=\dfrac{1}{2} × t_1 × 10##

##A_2=\dfrac{1}{2} × t_2 × (20+10)##

##A_3= 24 × 20##

##555=10t_2+15t_2+480##

##75=25t_2##

##t_2=3## seconds

##t_{total}=6+3+24=33##seconds

For part (d),

##a=\dfrac{10}{3}=3\frac{1}{3} m/s^2##

Cheers! Bingo!
Yes, there does appear to be some math error.

I see that you skipped part (b), but the title of the thread,

"Solve the given problem involving the velocity-time graph",

does promise a graph.
 
  • #3
SammyS said:
Yes, there does appear to be some math error.

I see that you skipped part (b), but the title of the thread,

"Solve the given problem involving the velocity-time graph",

does promise a graph.
part (b) is fine with me...i was interested on the highlighted part. I amended the thread title...

Cheers @SammyS
 
  • #4
chwala said:
part (b) is fine with me...i was interested on the highlighted part. I amended the thread title...

Cheers @SammyS
I agree with a and c.
But I think in part d you've made a mistake.
You said a=10/t1 so a should be equal to 10/6.
 
  • Like
Likes chwala

1. What is the formula for finding total time taken in kinematics?

The formula for finding total time taken in kinematics is t = (v-u)/a, where t is the total time taken, v is the final velocity, u is the initial velocity, and a is the acceleration.

2. How do you calculate acceleration in kinematics?

To calculate acceleration in kinematics, you can use the formula a = (v-u)/t, where a is the acceleration, v is the final velocity, u is the initial velocity, and t is the total time taken.

3. Can the total time taken be negative in kinematics?

No, the total time taken cannot be negative in kinematics. Time is a scalar quantity and cannot have a negative value. If the result of the calculation is negative, it means that the initial velocity and final velocity have opposite directions, indicating a change in direction rather than a total time taken.

4. How does the value of acceleration affect the total time taken in kinematics?

The value of acceleration affects the total time taken in kinematics as a higher acceleration will result in a shorter total time taken, while a lower acceleration will result in a longer total time taken. This is because acceleration is directly proportional to the change in velocity and inversely proportional to the total time taken.

5. Can you use kinematics to find the total time taken for a body in free fall?

Yes, kinematics can be used to find the total time taken for a body in free fall. In this case, the acceleration due to gravity is used as the value of acceleration in the kinematics equations. The initial velocity is usually taken as 0, and the final velocity is the velocity at which the body hits the ground. The total time taken can then be calculated using the formula t = √(2h/g), where h is the height of the object and g is the acceleration due to gravity.

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