Motion under gravity:
When the particle is thrown vertically upwards then it comes back because of the gravity. This motion of the particle is because of the acceleration g. When the particle is moving upward, the value of g is negative and when it comes back, the value of g is positive. At the maximum height velocity of a particle is zero. The value of g is 9.8 m/s2.
Illustration: A ball is thrown upwards which returns back after 8 seconds. on Earth. If the equation of motion is s = ut - 4.9 t2, where s is in meter and t in seconds. then find velocity at t = 0 and t = 2.
Solution : As it comes back after 8 seconds.
∴ distance covered in 8 seconds. is 0.
∴ s = ut - 4.9 t2 . . . (i)
or 0 = u x 8 - 4.9 x 82
or u = (4.9 x 8 x 8) / 8 = 39.2m/s
Differentiating,
ds/dt = u-4.9 x 2t
or or v = ds/dt = 39.2 - 9.8t
∴ velocity at t = 0= 39.2 - 9.8 x 0 = 39.2m/s
velocity at t = 2 = 39.2 - 9.8 x 2 = 19.6m/sm/s.
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