# …the study of the motion of objects without describing the causes. Kinematics.

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…the study of the motion of objects without describing the causes. Kinematics

Important Variables SymbolVariableSI unit ttimes x 0 OR y 0 Initial positionm x OR ydisplacementm v0v0 initial velocitym/s vfinal velocitym/s aaccelerationm/s 2

Kinematic Equations for Constant Acceleration

Acceleration, Direction, and Signs

Sample Problem #1 From the moment a 40 m/s fastball touches the catcher’s mitt until it is completely stopped takes 0.012 s. Calculate the average acceleration of the ball as it is being caught.

Sample Problem #2 A race car accelerates from rest at +7.5 m/s 2 for 4.5 s. How fast will it be going at the end of that time?

Sample Problem #3 A bullet accelerates at 68,000 m/s 2 from rest as it travels the 0.80 m of the rifle barrel. How long was it in the barrel?

Sample Problem #4 A motorcycle traveling at 16 m/s accelerates at a constant rate of 4.0 m/s 2 over 50 m. What is its final velocity?

Sample Problem #5 A car starts from rest and accelerates uniformly at a rate of a for a time t and travels a distance d. If the rate of acceleration is doubled the distance traveled will be closet to which of the following?

Sample Problem #6 An arrow leaves a bow with a speed of 42 m/s. Its velocity is reduced to 34 m/s by the time it hits its target. How much distance did the arrow travel over if it were in the air for 2.4 seconds?

Free-fall Conditions The object is accelerating in a downward direction. Gravity is the only force acting on the object. Acceleration is constant, assuming that there is no air resistance. The acceleration is due to gravity. a g = g = 9.8 m/s 2 g is expressed as either + or – depending on the context of the situation.

Sample Problem #7 To calculate the depth of a well a physics student drops a rock into the well. 3.8 seconds after the rock is dropped the student sees it hit the bottom. How deep is the well? How fast is the rock traveling the instant before it hits the bottom?

Sample Problem #8 The speed limit in a school zone is 40 km/h (about 25 mph). A driver traveling at this speed sees a child run into the road 13 m ahead of his car. He applies the brakes, and the car decelerates at a uniform rate of 8.0 m/s 2. If the driver’s reaction time is 0.25 s, will the car stop before hitting the child?

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