# General motion in a straight line

• MHB
• Shah 72
In summary, the conversation discusses calculating the distance traveled by an object using integration. The process involves finding the velocity and integrating it over specific time intervals. However, there is a discrepancy between the calculated distance and the textbook answer. Both individuals are unsure of the exact solution and suggest the possibility of a calculation error or incorrect answer in the textbook.
Shah 72
MHB

I calculated (a)
I don't know how to calculate (b)

after integrating both of them you will get this

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DaalChawal said:
after integrating both of them you will get this
Thank you so so so so much! That was so so helpful!

DaalChawal said:
after integrating both of them you will get this
Can you also pls tell how to calculate 7(c).
I calculate s1 for interval between t=0 and t=1 and s2 for the interval between t=1 and t=5 by integrating their respective velocities. I did that and I get the ans 30m but the textbook ans is 69.2m. Pls help

For $0 \le t \lt 1$ $s= 1/2 t^2 + 2/3 t^3$ putting t=1 we get 7/6
For $1 \le t \le 5$ $v= 30/4 t + 5/4 t^{-2} - 23/4$ integrate and putting limits we get $x-7/6 = (15/4) (5^2 - 1^2) + (5/4)(1- 1/5)+ (23/4)(1-5)$ I'm getting x =63 + $7 \over 6$ So total distance = 63 + $7 \over 3$ = 65.34
Even I am also not getting the answer may be I made a calculation mistake or the answer is wrong. Afaik this will be done here.

DaalChawal said:
For $0 \le t \lt 1$ $s= 1/2 t^2 + 2/3 t^3$ putting t=1 we get 7/6
For $1 \le t \le 5$ $v= 30/4 t + 5/4 t^{-2} - 23/4$ integrate and putting limits we get $x-7/6 = (15/4) (5^2 - 1^2) + (5/4)(1- 1/5)+ (23/4)(1-5)$ I'm getting x =63 + $7 \over 6$ So total distance = 63 + $7 \over 3$ = 65.34
Even I am also not getting the answer may be I made a calculation mistake or the answer is wrong. Afaik this will be done here.
Thank you very much!

## 1. What is general motion in a straight line?

General motion in a straight line is the motion of an object that moves in a single direction without changing its path or speed. This type of motion is often represented by a straight line on a graph.

## 2. What is the difference between uniform and non-uniform motion in a straight line?

Uniform motion in a straight line is when an object moves at a constant speed in a straight line, while non-uniform motion is when an object changes its speed or direction while moving in a straight line.

## 3. How is velocity calculated in general motion in a straight line?

Velocity in general motion in a straight line is calculated by dividing the displacement of an object by the time it takes to travel that distance. It is represented by the formula v = d/t, where v is velocity, d is displacement, and t is time.

## 4. What is the difference between speed and velocity in general motion in a straight line?

Speed is a measure of how fast an object is moving, while velocity is a measure of both speed and direction. In general motion in a straight line, speed is calculated by dividing the distance traveled by the time taken, while velocity is calculated by dividing the displacement by the time taken.

## 5. How does acceleration affect general motion in a straight line?

Acceleration is the rate of change of velocity and it affects general motion in a straight line by causing an object to either speed up or slow down. If the acceleration is in the same direction as the motion, the object will speed up, and if it is in the opposite direction, the object will slow down.

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