Answered

7. In a 100m race Usain Bolt and Assefa Powel cross the finish line in a dead beat, both taking 10s Accelerating uniformly, Usain Bolt takes 3s and Assefa Powel took 2s to attain maximum speed which they maintained for the rest of the race. What was the acceleration of Usain Bolt and Assefa Powel respectively? B)4.92 m/s, 15m / (s ^ 2)

A. 4.32 m/s², 2.25m / (s ^ 2)

C)3.92m / (s ^ 2) 555m / (s ^ 2)

D. 4.92 m/s²,535m/s^2



Answer :

Answer:

  • the acceleration of Usain Bolt = 3.92 m/s²
  • the acceleration of Assefa Powel = 5.55 m/s²

the answer = C

Explanation:

We can find the acceleration of Usain Bolt and Assefa Powel by using the linear motion formulas.

For linear motion with constant velocity:

[tex]\boxed{v=v_o}[/tex]

[tex]\boxed{s=s_o+v_ot}[/tex]

For linear motion with constant acceleration:

[tex]\boxed{v=v_o+at}[/tex]

[tex]\boxed{s=s_o+v_ot+\frac{1}{2}at^2 }[/tex]

where:

  • [tex]v[/tex] = final velocity
  • [tex]v_o[/tex] = initial velocity
  • [tex]s[/tex] = final position / distance
  • [tex]s_o[/tex] = initial position
  • [tex]t[/tex] = time
  • [tex]a[/tex] = acceleration

For Usain Bolt:

  • the first 3 seconds ([tex]t_1[/tex]) is linear motion with constant acceleration, whereas the rest of 7 seconds ([tex]t_2[/tex]) is linear motion with constant acceleration ⇒ the total time is 10 seconds.
  • [tex]t_1[/tex] = 3 s
  • [tex]t_2[/tex] = 10 - 3 = 7s
  • [tex]s[/tex] = 100 m
  • [tex]v_o_1[/tex] = 0

For 1st to 3rd second:

[tex]v_o_2=v_o_1+at_1[/tex] (the final velocity of 3rd second will become the initial velocity of the 4th second)

[tex]v_o_2=0+a(3)[/tex]

[tex]\bf v_o_2=3a[/tex]

[tex]s_1=s_o+v_o_1t_1+\frac{1}{2}at_1^2[/tex]

[tex]s_1=0+0+\frac{1}{2} a(3)^2[/tex]

[tex]\displaystyle\bf s_1=\frac{9}{2} a[/tex]

For 4th to 10th second:

[tex]s=s_1+v_o_2t_2[/tex]

[tex]100=\frac{9}{2} a+3a(7)[/tex]

[tex]100=\frac{51}{2} a[/tex]

[tex]\displaystyle a=100\div\frac{51}{2}[/tex]

[tex]\bf a=3.92\ m/s^2[/tex]

For Assefa Powel:

  • the first 2 seconds ([tex]t_1[/tex]) is linear motion with constant acceleration, whereas the rest of 8 seconds ([tex]t_2[/tex]) is linear motion with constant acceleration ⇒ the total time is 10 seconds.
  • [tex]t_1[/tex] = 2 s
  • [tex]t_2[/tex] = 10 - 2 = 8s
  • [tex]s[/tex] = 100 m
  • [tex]v_o_1[/tex] = 0

For 1st to 2nd second:

[tex]v_o_2=v_o_1+at_1[/tex] (the final velocity of 2nd second will become the initial velocity of the 3rd second)

[tex]v_o_2=0+a(2)[/tex]

[tex]\bf v_o_2=2a[/tex]

[tex]s_1=s_o+v_o_1t_1+\frac{1}{2}at_1^2[/tex]

[tex]s_1=0+0+\frac{1}{2} a(2)^2[/tex]

[tex]\bf s_1=2a[/tex]

For 3rd to 10th second:

[tex]s=s_1+v_o_2t_2[/tex]

[tex]100=2a+2a(8)[/tex]

[tex]100=18a[/tex]

[tex]a=100\div18[/tex]

[tex]\bf a=5.55\ m/s^2[/tex]