Physics Exercises/Kinematics in One Dimension

Kinematics in one dimension involves motion where the position can be represented by a single number. Motion in other directions (if any) are ignored. For solving kinematics problems without calculus, use of following equations is necessary (these can be derived using calculus):

$\begin{array}{cc}{v}_f& =at+v_i\\ x_f& =(1/2)a{t}^2+v_{i}t+x_i\\ v_f^2& =v_i^2+2at\end{array}$.

Without Calculus

1. A man fires a rock out of a slingshot directly upward. The rock has an initial velocity of 15 m/s. How long will it take for the rock to return to the level he fired it at?
2. It takes a man 10 seconds to ride down an escalator. It takes the same man 15 s to walk back up the escalator against its motion. How long will it take the man to walk down the escalator at the same rate he was walking before?

With Calculus

1. Starting with the definitions of velocity and acceleration, derive the kinematics equation for constant acceleration x = x₀ + v₀t + (1/2) a t².
2. A cockroach starts 1 cm away from a wall. It starts running in a line directly away from the wall with a velocity of 1 cm/s, acceleration of 1 cm/s^2, jerk (d³x/dt³) of 1 cm/s³, d⁴x/dt⁴ of 1 cm/s^4, and so on. How far is the cockroach from the wall after 1 s?

References

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