Physics equations/02-One dimensional kinematics/A:practice

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Highway exits[edit]

A driver gets on mile 25 of a highway at 3:30 pm and exits at mile 150 at 5:30 pm. If the road is straight, what is the velocity and is it average or instantaneous?

Finding average velocity[edit]

A particle starting 23 m from the origin has moved to 43 m in 5 s. Find .

Finding the average acceleration if the direction reverses in the time interval[edit]

A person is jogging east at 3m/s when he suddenly reverses direction and is jogging west at 3m/s, taking one second to accomplish this reversal. Take east to be the 'positive' direction. What is the average acceleration?

Proving one of the equations of motion[edit]

Use algebra to show that

 and 

implies

 and  .

CALCULUS: Motion and the mathematical definition of derivative as a limit[edit]

By definition, velocity involves two different positions at two different times. However, we may take the limit that these differences are very small and define the instantaneous velocity.

A connection to differential calculus is seen by rewriting and as and , so that :

CALCULUS: Problem involving velocity, acceleration, and equations of motion[edit]

A particle's motion[1] is described by the equation . Find

a) the particle's velocity function,

b) its instantaneous velocity at t = 2 s. Also find

c) the particle's acceleration function and

d) its instantaneous acceleration at t = 2 s.

  1. https://en.wikibooks.org/w/index.php?title=Physics_with_Calculus/Mechanics/Motion_in_One_Dimension&oldid=2403866