Question

The distance S (in kms) travelled by a particle in time ‘t’ hours is given S(t) = $\dfrac{{{t^2} + t}}{2}$. Find the distance travelled by the particle after
i.Three and half hours.
ii.Eight hours and fifteen minutes.

Answer 1

Hint: In this question we have given the distance (S) travelled by the particle in time ‘t’ hours is $\dfrac{{{t^2} + t}}{2}$. To find the distance travelled by the particle after three hours and half hours and Eight hours and fifteen minutes, we only need to put the value of time in place of ‘t’ in this formula $\dfrac{{{t^2} + t}}{2}$.

Complete step-by-step answer:
We have given the distance S (in km) travelled by a particle in time ‘t’ hours is S(t) = $\dfrac{{{t^2} + t}}{2}$
i.Distance travelled by the particle after three and half hours = $\dfrac{{{t^2} + t}}{2}$
= $\dfrac{{{{(3.5)}^2} + 3.5}}{2} = \dfrac{{15.75}}{2}$= 7.87 km
Hence, the distance travelled by the particle after three and half hours is 7.87 km.

ii.Distance travelled by the particle in eight hours and fifteen minutes.
First, we have to convert 8 hours & 15 minutes into an hour.
60 min = 1 hours
15 min = $\dfrac{1}{{60}} \times 15 = \dfrac{1}{4}$hours
8 hours and 15 min = $8 + \dfrac{1}{4} = \dfrac{{33}}{4}$= 8.25 hours
Now, distance travelled by the particle in 8.25 hours = $\dfrac{{{t^2} + t}}{2}$
= $\dfrac{{{{(8.25)}^2} + 8.25}}{2} = \dfrac{{68.06 + 8.25}}{2}$ = $\dfrac{{76.31}}{2}$= 38.155 km
Hence, the distance travelled by the particle after eight hours and fifteen minutes is 38.155 km.

Note: Try to convert time into hours because time which is given in the question is in terms of hours. So, you have to convert minutes into hours. Then you have to put the value of time in $\dfrac{{{t^2} + t}}{2}$. As you can see in the above question, we have written three hours and half hours = 3.5 hours and eight hours and fifteen minutes = 8.25 hours.