Question

a particle is thrown vertically upwards with speed 20m/s the speed of the particle is 10m/s after time

Answer 1

Approximately 2 seconds if consider acceleration of gravity to be 10 m/sec.

Answer 2

Let t be time
v- final velocity=10m/s
u-initial velocity=20m/s
s-distance covered in that time.

Taking upward as +ve direction

${v}^{2} - {u}^{2} = - 2gs \\ 100 - 400 = 2 \times 10 \: s \\ s = 15m$
now we have to find in how much time it reached 15 m.

so,
$s = ut - \frac{1}{2} g {t}^{2} \\ 15 = 20t - 5 {t}^{2} \\ {t}^{2} - 4t + 3 = 0 \: \\ (t - 1)(t - 3) = 0$
so either t=1sec. or t=3sec.