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acceleration problems use your acceleration formulas to answer the foll…

Question

acceleration problems
use your acceleration formulas to answer the following questions. unless
otherwise stated, convert all units to si units.

  1. while traveling along a highway, a driver slows down from 24 m/s to 15 m/s in 12

seconds. what is the automobiles acceleration? (remember that a negative
acceleration indicates a slowing down or deceleration.)

  1. a parachute on a racing dragster opens and changes the speed of the car from 85 m/s

to 45 m/s in a period of 4.5 seconds. what is the acceleration of the dragster?

  1. the table below includes data for a ball rolling down a hill. fill in the missing data values

in the table following the pattern that the existing data shows and determine the
acceleration of the ball.
acceleration = _

Explanation:

Step1: Determine the acceleration formula

The formula for acceleration is \(a=\frac{v - u}{t}\), where \(v\) is the final velocity, \(u\) is the initial velocity, and \(t\) is the time.

Step2: Solve for problem 1

Given \(u = 24\space m/s\), \(v=15\space m/s\), \(t = 12\space s\).
Substitute into the formula: \(a=\frac{15 - 24}{12}=\frac{-9}{12}=- 0.75\space m/s^{2}\)

Step3: Solve for problem 2

Given \(u = 85\space m/s\), \(v = 45\space m/s\), \(t=4.5\space s\)
Substitute into the formula: \(a=\frac{45 - 85}{4.5}=\frac{-40}{4.5}\approx - 8.89\space m/s^{2}\)

Step4: Solve for problem 3

From the table, when \(t = 2\space s\), \(v = 3\space m/s\). Using \(a=\frac{v - u}{t}\) with \(u = 0\space m/s\) (initial speed at \(t = 0\)), \(a=\frac{3-0}{2}=1.5\space m/s^{2}\)
Check with \(t = 10\space s\), \(v=15\space m/s\), \(a=\frac{15 - 0}{10}=1.5\space m/s^{2}\)
For the missing time when \(v = 9\space m/s\), using \(t=\frac{v - u}{a}\) (\(u = 0\)), \(t=\frac{9 - 0}{1.5}=6\space s\)
For the missing speed when \(t = 8\space s\), using \(v=u+at\) (\(u = 0\)), \(v=0 + 1.5\times8=12\space m/s\)

Answer:

  1. \(-0.75\space m/s^{2}\)
  2. \(-8.89\space m/s^{2}\)
  3. Missing time: \(6\space s\), missing speed: \(12\space m/s\), Acceleration: \(1.5\space m/s^{2}\)