Velocity and Acceleration (t,v) graph HELP please

In summary, the conversation discusses a car traveling at a constant acceleration of a m/s/s from point A to point B with a speed of 10m/s and then traveling at a constant speed of Vm/s for 10 seconds until reaching point C. From there, the car continues to travel with a constant acceleration of 3a m/s/s for T seconds until reaching a speed of 20 m/s at point D. The [t,v] graph for the motion shows that V=12.5 and the distance from A to D is 675m. Through simultaneous equations and using the equation for velocity, it is possible to determine the values of a and T. The area under the graph of velocity is the distance traveled,
  • #1
As a car passes point A on a straight road, it's speed is 10m/s, the car moves with constant acceleration, a m/s/s, along the road for T seconds until it reaches point B, where it's speed is Vm/s.
The car travels at this speed for a further 10 seconds, when it reaches the point C. From C it travels for a further T seconds with constant acceleration 3a m/s/s until it reaches a speed of 20 m/s at the point D.

Sketch the [t,v] graph for the motion, and show that V=12.5

I had no problem with showing V = 12.5 through a simultaneous equation.

However part B states,
The distance from A to D is 675m, find a and T

Any help will be so very greatly appreciated!
Thanks in advance
New2Science
 
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  • #2
The area under the graph of velocity is the distance traveled. The area, as should be obvious from the sketch, is a sum of three simple areas. Together with the equation you used for velocity, you should be able to determine a and T from it.
 
  • #3
If you can sketch the [t,v] graph for the motion, then you can deduce the answer.
The area under the graph is the distance.
 
  • #4
Thanks a lot for the help!

I got it now (:

Thanks Again
 
  • #5


I would approach this problem by first understanding the definitions of velocity and acceleration. Velocity is the rate of change of an object's position over time, while acceleration is the rate of change of an object's velocity over time.

Based on the given information, we know that the car starts at point A with a velocity of 10m/s and reaches a velocity of 20m/s at point D. This means that the car has undergone a change in velocity of 10m/s over a period of T seconds. Using the formula for acceleration, a = (Vf - Vi)/t, we can solve for T:

T = (20m/s - 10m/s)/a = 10/a

We also know that the car travels at a constant acceleration of 3a m/s/s for T seconds from point C to point D. Using the formula for distance, d = Vi*t + 0.5*a*t^2, we can calculate the distance traveled from point C to point D:

675m = 20m/s*T + 0.5*3a m/s/s*(T^2)

Substituting T = 10/a, we get:

675m = 20m/s*(10/a) + 0.5*3a m/s/s*((10/a)^2)

Simplifying the equation, we get:

675 = 200/a + 15/a^2

Multiplying both sides by a^2 and rearranging the equation, we get a^2 + (200/675)*a - 45 = 0

Solving for a using the quadratic formula, we get two possible values for a: a = 2.5 m/s/s or a = -18 m/s/s. However, since the car is accelerating in a positive direction, we can eliminate the negative value and conclude that a = 2.5 m/s/s.

Plugging this value back into our equation for T, we get:

T = 10/a = 10/(2.5 m/s/s) = 4 seconds

Therefore, the car accelerates at 2.5 m/s/s for 4 seconds from point A to point B, travels at a constant velocity of 20 m/s for 10 seconds from point B to point C, and accelerates at 7.5 m/s/s for 4 seconds from point C to point D.

To summarize, the
 

1. What is the difference between velocity and acceleration?

Velocity is a measure of the rate of change of an object's displacement with respect to time. It tells us how fast and in what direction an object is moving. Acceleration, on the other hand, is a measure of the rate of change of an object's velocity with respect to time. It tells us how much an object's velocity is changing over time.

2. How is velocity represented on a (t,v) graph?

Velocity is represented by the slope of a line on a (t,v) graph. The steeper the slope, the greater the velocity. A positive slope indicates an object is moving in the positive direction, while a negative slope indicates the object is moving in the negative direction.

3. What does a horizontal line on a (t,v) graph represent?

A horizontal line on a (t,v) graph represents an object with constant velocity. This means that the object is not changing its speed or direction, and is moving at a constant rate.

4. How is acceleration represented on a (t,v) graph?

Acceleration is represented by the curvature of a line on a (t,v) graph. A curved line indicates that the velocity is changing, and the amount of curvature indicates the rate of acceleration. A steeper curve indicates a higher rate of acceleration.

5. What is the relationship between velocity and acceleration on a (t,v) graph?

Velocity and acceleration are related by the fundamental equation of motion, which states that acceleration is equal to the rate of change of velocity. This means that the slope of a (t,v) graph represents acceleration, and the area under the curve represents velocity.

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