Question

The displacement (in meters) of a particle moving in a straight line is given by S= t^2 - 7t + 17 ii)iii)iv)

Answer 1

Given displacement of a particle moving in a straight line,

`S=t^2-7t+17`

(i) Calculate the average velocity in the interval [3,4]

`\begin{gathered} \text{Average velocity = }(S(4)-S(3))/(4-3) \\ \text{Average velocity = }(\lbrack(4)^2-7*4+17\rbrack-\lbrack(3)^2-7*3+17\rbrack)/(4-3) \\ \text{Average velocity =}(5-5)/(1) \\ \text{Average velocity = 0 m/s} \end{gathered}`

(iii) Calculate the average velocity in the time interval [4,5].

`\begin{gathered} \text{Average velocity = }(S(5)-S(4))/(5-4) \\ \text{Average velocity = }(\lbrack(5)^2-7*5+17\rbrack-\lbrack(4)^2-7*4+17\rbrack)/(5-4) \\ \text{Average velocity = }(7-5)/(1) \\ \text{Average velocity = }2 \end{gathered}`

(iv) Calculate the average velocity in the time interval [4,4.5].

`\begin{gathered} \text{Average velocity = }(S(4.5)-S(4))/(4.5-4) \\ \text{Average velocity = }(\lbrack(4.5)^2-7*4.5+17\rbrack-\lbrack(4)^2-7*4+17\rbrack)/(4.5-4) \\ \text{Average velocity = }(5.75-5)/(0.5) \\ \text{Average velocity = }1.5 \end{gathered}`