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: \(1.5\space m/s^{2}\)