Solving accelerated motion problems

We now have two equations that together make up a mathematical model of motion that includes position, velocity, acceleration, and time. Equation (4.2) describes velocity and equation (4.3) describes position. Read the text aloud
Model for accelerated motion
How far does the car go before it reaches a speed of 30 m/s?Some problems require both equations. For example, consider a car that starts from rest with a constant acceleration of 5 m/s2. How far does the car go before it reaches a speed of 30 m/s (67 mph)? This problem asks for a distance but it gives you speed and acceleration. There are two unknown values: time and position. Therefore, to solve the problem you need both equations.
  1. Equation (4.2) allows you to solve for the time in terms of the known final velocity and acceleration.
  2. Equation (4.3) gives you the position.
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A car starts at rest at the top of a ramp. What is the acceleration if the car goes 1.4 m down the ramp in 1.6 seconds?A car starts at rest at the top of a ramp. What is the acceleration if the car goes 1.4 m down the ramp in 1.6 s?
  1. You are given position, time, and an initial velocity of zero. You only need equation (4.3) since there is only one unknown variable.
  2. Solve the equation for acceleration to find that a = 1.09 m/s2.
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A car starts at rest at the top of a ramp that creates an acceleration of 2.1 m/s2. How much time does it take the car to travel 1 meter?A car starts from rest at the top of a ramp that creates an acceleration of 2.1 m/s2. How much time does it take the car to travel 1 m?
  1. You only need equation (4.3) since there is only one unknown variable.
  2. Solve the equation for acceleration and substitute values to find that t =  0.98 s.
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