Question

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.

Answer 1

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 $- 0.1250 cm/s^2$

Answer 2

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

Further explanation

Acceleration is rate of change of velocity.

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

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

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem !

Given:

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

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

Conclusion:

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

Learn more

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

Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

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