Question

body initially at rest starts moving with constant acceleration of 2 metre per second. Calculate

1 the velocity acquired and

2 the distance travelled in 5 seconds

Answer 1

1) Let a is the acceleration,
here,
a = 2 m/s²
we know,

a = dv/dt [ rate of change of velocity ]

dv/dt = 2
dv = 2dt
integrate,
Vf - Vi = 2[ t ] time 0 to 5 sec -------(1)

Vi = 0 { initial velocity = 0,
so,
Vf = 2 [ 5 - 0 ] = 2 × 5 = 10 m/s
hence, velocity after 5 sec = 10 m/s

(2) v = 2t from eqn (1)
dx/dt = v [ rate of change of displacement ]

dx/dt = 2t
dx = 2t.dt
integrate,

xf - xi = t²
at t = 0 => xi = 0
so,

xf = t²
xf = 5² = 25 m

hence, displacement = 25m