Question

A particle’s velocity is given (in units of meters per second) by the function
v = 1 + (t^3)/10 – (t^2)/20
Find the distance travelled from t = 0 and t = 2.

Answer 1

Answer:

Step-by-step explanation:

distance is velocity times time.

as velocity also changes with time, total distance will be the sum of all the differential distances during the interval as the time period becomes vanishingly small. In other words the integral over 0 ≤ t ≤ 2 of vdt

$d = \int\limits^2_0 {1 + \frac{1}{10} t^3} - \frac{1}{20} t^2 \, dt$

d = t + $\frac{1}{40}$t⁴ - $\frac{1}{60}$t³ $\left \{ {{t=2} \atop {t=0}} \right$

d = 2 + $\frac{1}{40}$(2)⁴ - $\frac{1}{60}$(2)³ - (0 + $\frac{1}{40}$(0)⁴ - $\frac{1}{60}$(0)³)

d = 2 + $\frac{16}{40}$ - $\frac{8}{60}$

d = 2 $\frac{8}{15}$ m