# Physics Exercises/Kinematics in One Dimension

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**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):

## Without Calculus[edit]

- 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?
- 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?
- A man riding a bicycle at a speed of 25 km/h passes a parked car. When the bicycle is 100 m ahead of the car, the car starts. The car instantly accelerates to a speed of 50 km/h, and subsequently maintains that speed. Find out when and where the car passes the bicycle, using both a graphical method and an arithmetical method.
- Cinderella leaves the ball at quarter to twelve in a coach travelling at a speed of 12 mph. Five minutes later the prince also leaves the ball following her. Calculate the speed at which the prince reaches her just as the clock strikes twelve.
- Two sporty snails are having a race. Because one of them is a famous sprinter, the other is given a head start of 1.0 meters. 15 minutes after the start of the race the sprinter catches up with the slower one. The sprinter was creeping at a speed of 60 cm/min. Calculate the speed of the slower snail.
- Miss Anna Litical wants to meet a friend living 150 miles away. She starts at 8:30 with an average speed of 50 mph. Her friend starts 30 minutes later travelling at a speed of 35 mph. When and where do they meet?

## With Calculus[edit]

- Starting with the definitions of velocity and acceleration, derive the kinematics equation for constant acceleration
*x*=*x*_{0}+*v*_{0}*t*+ (1/2)*a t*^{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 (
*d*^{3}*x*/*dt*^{3}) of 1 cm/s^{3},*d*^{4}*x*/*dt*^{4}of 1 cm/s^4, and so on. How far is the cockroach from the wall after 1 s?