2. 1D Motion / Kinematics

Which of the following best explains why quick acceleration can increase fuel consumption by $2\text{ miles per gallon;}$?

Starting from rest, a car accelerated to 20m/s in 4s. What was the magnitude of the car's constant acceleration?

A rocket starts from rest and moves upward from the surface of the earth. For the first $10.0$ s of its motion, the vertical acceleration of the rocket is given by $a_{y}=(2.80$ m/s³$)t$, where the $+y$-direction is upward. What is the speed of the rocket when it is $325$ m above the surface of the earth?

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.

A particle's velocity is given by the function $\(\mathcal{v}\)_x = (2.0 \, \(\text{m/s}\)) \(\sin\)(\(\pi\) t)$, where $t$ is in $s$. What is the particle's acceleration at that time?