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Question

A particle is moving with uniform acceleration. Its displacement at any instant t is given as s=10t+49t2. What is the initial velocity, velocity at t=3 sec and uniform acceleration?

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Solution

Given:
Acceleration is uniform.
Displacement is given by
s=10t+49t2

According to second equation of motion,
s=ut+12at2

On comparing coefficients,
ut=10tu=10 m/s and
12at2=49t2a=2×49=98 m/s2

Velocity at t=3sec has be found.
By first equation of motion,
v=u+at
v=10+98(3)=304 m/s

Thus,
  • initial velocity u=10 m/s
  • velocity vt=3=304 m/s
  • uniform acceleration a=98 m/s2

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