Aturtle 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/s 2)t2. find the turtle's initial acceleration.

Acceleration is rate of change of velocity.

The equation of turtle's position as a function of time is given by:

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

Differentiating further, we would get the equation for acceleration:

Therefore, initial acceleration is

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

Acceleration is rate of change of velocity.

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:

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

cm/s

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

cm/s²

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

Grade: High School

Subject: Physics

Chapter: Kinematics

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

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