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

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

What is the formula to find the total time taken in kinematics problems?

The formula to find the total time taken in kinematics problems often depends on the specific conditions given. Generally, for constant acceleration, you can use the equation \( t = \frac{v_f - v_i}{a} \), where \( v_f \) is the final velocity, \( v_i \) is the initial velocity, and \( a \) is the acceleration. If distance \( d \) and initial velocity \( v_i \) are given, you might use \( d = v_i t + \frac{1}{2} a t^2 \) to solve for \( t \).

How do I calculate acceleration in a kinematics problem?

Acceleration can be calculated using the formula \( a = \frac{v_f - v_i}{t} \), where \( v_f \) is the final velocity, \( v_i \) is the initial velocity, and \( t \) is the time taken. If distance \( d \) and time \( t \) are given, you can also use \( a = \frac{2(d - v_i t)}{t^2} \).

What information do I need to solve for total time and acceleration?

To solve for total time and acceleration in kinematics problems, you generally need at least three of the following variables: initial velocity (\( v_i \)), final velocity (\( v_f \)), acceleration (\( a \)), time (\( t \)), and distance (\( d \)). The specific equations you use will depend on which variables are given.

Can I use kinematic equations if the acceleration is not constant?

No, the standard kinematic equations assume constant acceleration. If the acceleration is not constant, you would need to use calculus-based methods to solve the problem, such as integrating the acceleration function to find velocity and position.

How do I approach solving a kinematics problem step-by-step?

To solve a kinematics problem step-by-step: 1. Identify the known and unknown variables.2. Choose the appropriate kinematic equations based on the known variables.3. Solve the equations algebraically to find the unknowns.4. Check the units and make sure the answers are physically reasonable.5. If necessary, use additional kinematic equations to find any remaining unknowns.

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