Question

A particle moving with a uniform acceleration its displacement at any instant t is given by S = 10t + 4.9t² what is 1)initial velocity
2) velocity at t=3 second
3) the uniform acceleration
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Answer 1

as s= ut +1/2at^2

1. u=10m/s

Answer 2

for this check out step by step explanation:

Explanation:

• Given , Velocity of a uniform body , S = 10t + 4.9t² , take as eqn........(1)
• From, law of kinematic, S = ut + 1/2 at² , take as eqn.......(2)
• Now , comparing eqn (1) and eqn (2). we get:

ut + 1/2 at² = 10t + 4.9t²

• Now, Taking : ut = 10t ( for comparing to get velocity , u = 10 ( As, t is common )
• Now , comparing acceleration, we get

Taking , 1/2 at² = 4.9 t² ( As, t² is common )

So, acceleration or 'a' = 4.9 × 2 = 9.8

• now , for uniform acceleration , as t = 3 second to moving a particle in it's acceleration
• So , V = ds/ dt = d(10t + 4.9t²)/dt

V = 10 + 4.9t

therefore, V = 10 + 2 × 4.9 × t ( as , 'a' = 2 × 4.9 = 9.8 )

V = 10 + 9.8 × t ( t = 3 )

V = 10 + 29.4 = 39.4 m/s²

Here , answers are

initial velocity as 'u' = 10 m/s¹

Acceleration as 'a' = 9.8 m/s²

Uniform acceleration as V = 39.4 m/s²

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