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 $x(t) = 50.0$ cm + ($2.00$ cm/s)$$$t$ − ($0.0625$ cm/s²)$t^2$. At what time $t$ is the velocity of the turtle zero?

A physics professor leaves her house and walks along the sidewalk toward campus. After $5$ min, it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E$2.10$. At which of the labeled points is her velocity constant and negative?

A race car starts from rest and travels east along a straight and level track. For the first $5.0$ s of the car's motion, the eastward component of the car's velocity is given by $v_x\left(t\right)=$ ($0.860$ m/s³)t². What is the acceleration of the car when $v_x=12.0$ m/s?

A physics professor leaves her house and walks along the sidewalk toward campus. After $5$ min, it starts to rain, and she returns home. Her distance from her house as a function of time is shown in Fig. E$2.10$. At which of the labeled points is her velocity decreasing in magnitude?

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 $x(t) = 50.0$ cm + ($2.00$ cm/s)$$$t$ − ($0.0625$ cm/s²)$t^2$. Sketch graphs of $x$ versus $t$, $v_x$ versus $t$, and $a_x$ versus $t$, for the time interval $t=0$ to $t=40$ s.

A car's velocity as a function of time is given by$v_x\left(t\right)=\alpha +\beta t^2$, where $\alpha =3.00$ m/s and $\beta =0.100$ m/s³. Calculate the average acceleration for the time interval $t=0$ to $t=5.00$ s.

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 $x\left(t\right)=50.0$ cm + ($2.00$ cm/s)$$$t$ − ($0.0625$ cm/s²)$t^2$. Find the turtle's initial velocity, initial position, and initial acceleration.