Question

a)Sketch a velocity-time graph to show this information.b)Use the velocity-time graph to find each of the following.The greatest velocity of the cyclist.C)The total time taken for the journey.d)The acceleration of the cyclist during the final stage.e)Find the average speed of the cyclist during the whole journey.

Answer 1

a)

b) 28 m/s

c) 60 sec

d) -2.8 m/s^2

e) 21 m/s

Explanation:

For t = 0 s to t = 20 s

a = 1.4 m/s ^2

u = 0 m/s

Therefore:

`\begin{gathered} v=u+at \\ \\ \text{ We replacing} \\ \\ v=0+1.4\cdot20 \\ \\ v=28\text{ m/s} \end{gathered}`

(a)

Knowing this, we can sketch the velocity-time graph:

(b)

The maximum speed can be determined in the graph and is 28 m/s

(c)

Area under v-t graph gives displacement:

`\begin{gathered} 1260=(1)/(2)(t+30)\cdot28 \\ t+30=1260\cdot(2)/(28) \\ t=90-30 \\ t=60\text{ s} \end{gathered}`

So the total time is 60 seconds

(d)

Using between t = 50 and t = 60

t = 60 - 50 = 10 sec

u = 28 m/s

v = 0

We solving for a:

`\begin{gathered} 0=28+a\cdot10 \\ \\ a=(-28)/(10) \\ \\ a=-2.8\text{ m/s}^2 \end{gathered}`

(e)

The average speed is the distance traveled in the total time, therefore:

`\begin{gathered} V=(d)/(t) \\ \\ \text{ We replacing} \\ \\ V=(1260)/(60) \\ \\ V=21\text{ m/s} \end{gathered}`