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A bicyclist and a runner are waiting at a red light. When the light turns green they start to speed up and the bicyclist gets to a final speed of 20 mph in 5 seconds. The runner gets to a final speed of 11 mph in 3 seconds. Which one had the greater acceleration?
the bicyclist or the runner.

Respuesta :

Answer:

The acceleration of bicyclist is greater than that of the runner.

Explanation:

It is given that,

Initial speed of both bicyclist and a runner is 0 as they both are waiting at a red light,

When the light turns green they start to speed up.

Final speed of the bicyclist is 20 mph in 5 seconds

The runner gets to a final speed of 11 mph in 3 seconds.

20 mph = 8.94 m/s

11 mph = 4.91 m/s

Acceleration of bicyclist is :

[tex]a_b=\dfrac{v}{t}\\\\a_b=\dfrac{8.94\ m/s}{5\ s}\\\\a_b=1.78\ m/s^2[/tex]

Acceleration of runner is :

[tex]a_r=\dfrac{v}{t}\\\\a_r=\dfrac{4.91\ m/s}{3\ s}\\\\a_r=1.63\ m/s^2[/tex]

It is clear that the acceleration of bicyclist is greater than that of the runner.

nuhulawal20

The acceleration of the bicyclist is 1.788m/s² and the acceleration of the runner is 1.639m/s².

Hence, the bicyclist has the greater acceleration.

Given the data in the question;

Since the runner and the bicyclist where initially at rest;

  • Initial velocity of bicyclist; [tex]u_b = 0[/tex]
  • Final velocity of bicyclist; [tex]v_b = 20mph = 8.9408m/s[/tex]
  • Time taken by the bicyclist; [tex]t_b = 5s[/tex]
  • Initial velocity of runner; [tex]u_r = 0[/tex]
  • Final velocity of runner; [tex]v_r = 11mph = 4.91744m/s[/tex]
  • Time taken by the runner; [tex]t_r = 3s[/tex]

Acceleration

Acceleration is simply the rate at which velocity changes with respect to time. Formula for acceleration can be derived from the First Equation of Motion;

[tex]v = u + at\\\\at = v - u\\\\a = \frac{v - u}{t}[/tex]

Where a is acceleration, v is final velocity, u is initial velocity and t is time elapsed.

Now, to determine who has the greater acceleration, we substitute our given values into the expression above.

For the bicyclist;

[tex]a_b = \frac{v -u}{t} \\\\a_b = \frac{ 8.9408m/s - 0}{5s}\\ \\a_b = \frac{8.9408m/s}{5s}\\ \\a_b = 1.788m/s^2[/tex]

For the runner;

[tex]a_r = \frac{v -u}{t} \\\\a_r = \frac{ 4.91744m/s - 0}{3s}\\ \\a_r = \frac{4.91744m/s}{3s}\\ \\a_r = 1.639m/s^2[/tex]

The acceleration of the bicyclist is 1.788m/s² and the acceleration of the runner is 1.639m/s².

Therefore, the bicyclist has the greater acceleration.

Learn more about Equation of Motion: https://brainly.com/question/18486505

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