# My attempt seems right? (Kinematics)

• IntegrateMe
In summary, a racing car traveling with constant acceleration increases its speed from 10m/s to 50m/s over a distance of 60m. Using the kinematic equation, the time it takes for the car to reach this speed is calculated to be 2 seconds.
IntegrateMe
A racing car traveling with constant acceleration increases its speed from 10m/s to 50m/s over
a distance of 60 m. How long does this take?

A. 2.0 s
B. 4.0 s
C. 5.0 s
D. 8.0 s
E. The time cannot be calculated since the speed is not constant

I did:

x - xo = 0.5 (Vo + V)(t)

Which is:

60 = 0.5 (60) (t)

Which is:

60 = 30t
t = 2

What am I doing wrong?

x=v0t+1/2*at^2

a= (v-v0)/t

combine and simplify
x=1/2(v+v0)t

t=(2x)/(v+v0)=2

Are you sure? The answers came from my college textbook, but I suppose they could be wrong?

Well, a constant acceleration makes for a velocity with a linear slope, and the slope of that velocity is by definition the acceleration (it's not even the mean acceleration as long as acceleration is constant). The slope of the velocity is ∆v/∆t=40/t m/s^2 (since t starts at 0).

Plug this into the kinematic equation, and, of course, you get the same thing as the algebra.
60=10*t+20*t

you can also get a directly
(v^2-v0^2)/(2*x)=a

a=20m/s^2

if you plug this into the quadratic kinematic equation

0=-60+10t+10t^2

t=-3,2 (-3 is non-physical)

Either way, as you've posted the problem, the answer is most definitely 2s.

Your attempt does seem to be on the right track, but there may be a small error in your calculation. Let's break down the equation you used: x - xo = 0.5 (Vo + V)(t). This equation is derived from the kinematic equation for displacement (x = xo + Vot + 0.5at^2), where x is the final position, xo is the initial position, Vo is the initial velocity, V is the final velocity, a is the acceleration, and t is the time.

In your calculation, you correctly substituted the given values for x, xo, and V into the equation. However, you used 60 m for both x and Vo, which is incorrect. The value of 60 m should only be used for x, as it represents the total displacement of 60 m. For Vo, you should use the initial velocity of 10 m/s.

So the correct equation would be: 60 m = 10 m/s + 0.5 (V)(t)

Solving for t, we get: t = (60 m - 10 m/s)/0.5V

Substituting the final velocity of 50 m/s, we get: t = (60 m - 10 m/s)/0.5(50 m/s) = 4 seconds.

Therefore, the correct answer is B. 4.0 s. Keep in mind that it is always important to carefully check your units and make sure they are consistent throughout your calculation. Good job on attempting to solve this problem using kinematics!

## 1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the cause of the motion, such as forces or energy. It involves describing the position, velocity, and acceleration of objects as they move through space and time.

## 2. How does kinematics relate to my attempt?

Kinematics is the study of motion, so it is directly related to your attempt. By understanding the principles of kinematics, you can analyze and evaluate your attempt to determine if it is correct or not.

## 3. What are the key concepts in kinematics?

The key concepts in kinematics include displacement, velocity, acceleration, and time. These quantities are used to describe the motion of objects and can be represented graphically using position-time, velocity-time, and acceleration-time graphs.

## 4. How can I use kinematics to improve my attempt?

By applying the principles of kinematics, you can analyze your attempt and determine where improvements can be made. For example, you can calculate the velocity and acceleration of the object in your attempt to see if they match the expected values based on the laws of kinematics.

## 5. What are some real-world applications of kinematics?

Kinematics has many real-world applications, including studying the motion of planets, analyzing the movement of vehicles, and designing roller coasters. It is also used in sports to improve performance and in robotics to program the movement of machines.

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