Question

Tasnova, the Devil, has entered a five mile race. She accelerates from the rest for the first 0.25 mile at a constant rate. Her time at the quarter mile was 133.7s. She runs the remainder of the race at a constant velocity. (1 mile=1609m.)Calculate Tasnova’s final velocity when she crosses the finish line.Calculate Tasnova’s time for the race.

Answer 1

Given data:

* The time taken by the Tasnova during the first quarter mile is 133.7 seconds.

* The initial velocity of the Tasnova is 0 m/s.

* The distance traveled in the constant acceleration part is,

`\begin{gathered} d=(1)/(4)\text{mile} \\ d=0.25\text{ mile} \\ d=0.25*1609\text{ meter} \\ d=402.25\text{ meter} \end{gathered}`

Solution:

(a). By the kinematics equation, the acceleration of the Tasnova during the first quarter mile is,

`d=ut+(1)/(2)at^2`

where u is the initial velocity, t is the time taken, a is the acceleration, and d is the distance traveled,

Substituting the known values,

`\begin{gathered} 402.25=0+(1)/(2)* a*(133.7)^2 \\ a=(402.25*2)/((133.7)^2) \\ a=0.045ms^(-2) \end{gathered}`

By the kinematics equation, the final velocity of the Tasnova is,

`v^2-u^2=2ad`

Substituting the known values,

`\begin{gathered} v^2-0=2*0.045*402.25 \\ v^2=36.2 \\ v=6.02ms^(-1) \end{gathered}`

As the value of velocity remains same after 133.7 seconds upto crossing the finish line.

Thus, the final velocity of the Tasnova is 6.02 meter per second.

(b). The distance remaining after the first quarter mile is,

`\begin{gathered} d^(\prime)=5-0.25 \\ d^(\prime)=4.75\text{ miles} \\ d^(\prime)=4.75*1609 \\ d^(\prime)=7642.75\text{ meters} \end{gathered}`

By the kinematics equation, the time taken by the Tasnova to travel 7642.75 meter is,

`\begin{gathered} v=(d^(\prime))/(t^(\prime)) \\ t^(\prime)=(d^(\prime))/(v) \end{gathered}`

Substituting the known values,

`\begin{gathered} t^(\prime)=(7642.75)/(6.02) \\ t^(\prime)=1269.56\text{ seconds} \end{gathered}`

Thus, the time taken by the Tasnova to complete the race is,

`\begin{gathered} T=t+t^(\prime) \\ T=133.7+1269.56 \\ T=1403.26\text{ seconds} \end{gathered}`

Hence, the time taken by the Tasnova to complete the race is 1403.26 seconds.