Question

The following data were collected during a short race between two friends. Velocity (m/s) 0 0.5 1 1.5 2 2 4 6 2 0 Time (s) 0 2 4 6 8 10 12 14 16 18 a) Describe the different sections of the graph. b) Determine the acceleration over the first eight seconds. c) Determine the maximum acceleration. d) Using the graph calculate the displacement: i) over the first eight seconds ii) the total race. e) Find the maximum velocity reached by the runner.

Answer 1

The characteristics of the kinematics allow to find the results for the questions about the movement of the body are:

a)  we have four sections;

• 0 to 8 s The body is accelerating.

• 8 to 10 s The body goes at a constant speed, the acceleration is zero.

• 10 to 14 Body accelerating.

• 14 to 18 Body slowing down.

b)  The acceleration is the first 8 s is:  a = 0.25 m / s²

c) The maximum acceleration is:    a = 1 m / s²

d) The displacement   is:  i) d₁ =  8m,     ii)  $d_{total}$= 16 m

e) maximum speed  is:      v = 6 m / s

Kinematics studies the movement of bodies by finding relationships between the position, speed and acceleration of bodies.

        v = v₀ + a t

        y = v₀ t + ½ a t²

where v and v₀ is the current and initial velocity, respectively, a is the acceleration and t is time.

In many circumstances graphs are made for their analysis, in a graph of speed versus time when we have a horizontal line the speed is constant, the acceleration is zero and in the case of a slope there is an acceleration, we have two cases:

• Positive slope the body is accelerating and the speed is increasing.

• Negative slope the body is stopping, the speed decreases.

Let's answer the different questions about the system.

a) in the attached we have a graph of the velocity versus time, each section corresponds to a change in the slope of the graph, we have four sections;

• 0 to 8 s The body is accelerating.

• 8 to 10 s The body goes at a constant speed, the acceleration is zero.

• 10 to 14 Body accelerating.

• 14 to 18 Body slowing down.

b) The acceleration is the first 8 s

          v = v₀ + a t

          $a = \frac{v-v_o}{\Delta t}$  

          $a = \frac{2-0}{8-0}$  

          a = 0.25 m / s²

c) The maximum acceleration is when the slope is maximum.

          $a = \frac{6-2}{ 14-10}$  

          a = 1 m / s²

Therefore the acceleration is maximum in the section between 10 and 14 s

d) The total displacement is the sum of the displacements of each section.

         $d_{total } = d_1 +d_2 + d_3 +d_4$  

We look for every displacement.

       d₁ = v₀ + ½ a₁ Δt²

       d₁ = 0 + ½ 0.25 8²

       d₁ = 8 m

In the second section the velocity is constant

         d₂ = v₂ Δt₂

         d₂ = 2 (10-8)

         d₂ = 4 m

The third section.

    d₃ = v₀ + ½ a t²

    d₃ = 2 + ½ 1 (14-10) ²

    d₃ = 10 m

The distance of the fourth section.

       

we look for acceleration

          a₄ = $\frac{v-v_o}{\Delta t}$  

          a₄ = $\frac{0-6}{18-14}$  

          a₄ = -1.5 m / s²

     

          d₄ = 6 + ½ (-1.5) (1814) ²

          d₄ = -6 m

The total displacement is;

          $d_{total}$ = 8 + 4 + 10 -6

          $d_{total}$ = 16 m

e) The maximum speed is the highest point in the graph of speed versus time that in the attachment we can see corresponds to

          v = 6 m / s

In conclusion using the characteristics of kinematics we can find the results for the questions about the motion of bodies are:

  a)  we have four sections;

• 0 to 8 s The body is accelerating.

• 8 to 10 s The body goes at a constant speed, the acceleration is zero.

• 10 to 14 Body accelerating.

• 14 to 18 Body slowing down.

b)  The acceleration is the first 8 s is:  a = 0.25 m / s²

c) The maximum acceleration is:    a = 1 m / s²

d) The displacement   is:  i) d₁ =  8m,     ii)  $d_{total}$= 16 m

e) maximum speed  is:      v = 6 m / s

Learn more about kinematics here: brainly.com/question/24783036