Question

the position of an object moving along X-axis is given by X=a+bt² where a=8.5m, b=2.5m/s² and t is measured in seconds. what is its velocity at t=0 s and t=2 s. what is the average velocity between t=2 s and t=4 s?^​

Answer 1

$$\begin{gathered} x=a+b{t}^2 \\ velocityatanyins\tan toftimeisgivenby: \\ v=\frac{dx}{dt} \\ v=2bt \\ att=0 \\ v=0 \\ att=2 \\ v=2\times 2.5\times 2=10m/s \\ dis\tan cetravelledbetween2to4secondsisgivenby \\ s=b(16-4)=12b=12\times 2.5=30m \\ timetaken=4-2=2s \\ averagevelocity=netdis\tan cetravelled/timetaken=30/2=15m/s \end{gathered}$$