2. 1D Motion / Kinematics

A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of $20$ m/s ($45$ mi/h) when it reaches the end of the $120$-m-long ramp. How much time does it take the car to travel the length of the ramp?

A car sits on an entrance ramp to a freeway, waiting for a break in the traffic. Then the driver accelerates with constant acceleration along the ramp and onto the freeway. The car starts from rest, moves in a straight line, and has a speed of $20$ m/s ($45$ mi/h) when it reaches the end of the $120$-m-long ramp. What is the acceleration of the car?

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 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 height of the rocket above the surface of the earth at $t=10.0$ 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 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 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 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?

A particle's velocity is described by the function vₓ = (t² - 7t + 10) m/s, where t is in s. What is the particle's acceleration at each of the turning points?

A good model for the acceleration of a car trying to reach top speed in the least amount of time is a_𝓍 = a_₀ ─ kv_𝓍, where a_₀ is the initial acceleration and k is a constant. Find an expression for the car's velocity as a function of time.

At this instant, the particle is speeding up and curving upward. What is the direction of its acceleration?

A sports car moving at constant velocity travels 120 m in 5.0 s. If it then brakes and comes to a stop in 3.7 s, what is the magnitude of its acceleration (assumed constant) in m/s², and in g's (g = 9.80 m/s²)?

The position of an object is given by 𝓍 = At + Bt², where 𝓍 is in meters and t is in seconds. What is the acceleration as a function of time?