Question

Velocity of a particle moving in a straight line varies with time t as we is equals to 3 + 2 t mper second the displacement covered in first three seconds

Answer 1

velocity of a particle moving in a straight line varies with time t as v = 3 + 2t

we know, velocity is the rate of change in displacement per unit time.
e.g., v = dx/dt

so, dx/dt = 3 + 2t

dx = (3 + 2t)dt

$\int\limits^3_0{dx}=\int\limits^3_0{3+2t}\,dt$

$x=3[t]^3_0+[t^2]^3_0$

x = 3 × 3 + (3² - 0²) = 9 + 9 = 18m

hence, displacement covered in first 3 second is 18m