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2 years ago

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A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right. the equation for

the turtle's position as a function of time is x(t)=50.0cm+(2.00cm/s)t−(0.0625cm/s2)t2. find the turtle's initial acceleration.

2 answers:

padilas [110]2 years ago

7 0

The turtle's initial acceleration is -0.125 cm/s²

<h3>Further explanation</h3>

Acceleration is rate of change of velocity.

$\large {\boxed {a = \frac{v - u}{t} } }$

$\large {\boxed {d = \frac{v + u}{2}~t } }$

<em>a = acceleration ( m/s² )</em>

<em>v = final velocity ( m/s )</em>

<em>u = initial velocity ( m/s )</em>

<em>t = time taken ( s )</em>

<em>d = distance ( m )</em>

Let us now tackle the problem !

<u>Given:</u>

$x = 50 + 2t - 0.0625t^2$

We will find the velocity function by deriving the displacement function above.

$v = \frac{dx}{dt}$

$v = 0 + 2 - 0.0625(2) t^{2-1}$

$v = 2 - 0.0625(2) t^{2-1}$

$v = 2 - 0.125t$ cm/s

Next, we will find the acceleration function by deriving the velocity function above.

$a = \frac{dv}{dt}$

$a = 0 - 0.125$

$a = -0.125$ cm/s²

<h3>Conclusion:</h3>

The turtle's initial acceleration is -0.125 cm/s²

<h3>Learn more</h3>

Velocity of Runner : brainly.com/question/3813437
Kinetic Energy : brainly.com/question/692781
Acceleration : brainly.com/question/2283922
The Speed of Car : brainly.com/question/568302

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate, Turtle , Initial , Differentiation

nadya68 [22]2 years ago

6 0

Answer: $- 0.1250 cm/s^2$

Acceleration is rate of change of velocity.

The equation of turtle's position as a function of time is given by: $x(t)=50+2t-0.0625t^2$

Differentiate the above equation to find the velocity as a function of time:

$\frac{dx}{dt}=v(t)=2-2\times 0.0625t$

Differentiating further, we would get the equation for acceleration:

$\frac{d^2x}{dt^2}=a(t)=-0.1250\\ \Rightarrow a(0)=-0.1250$

Therefore, initial acceleration is $- 0.1250 cm/s^2$

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