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Levart [38]
3 years ago
13

The acceleration of a point is given. a = 20 t m/s2 When t=0, s = 50 m and v = -8 m/s. What are the position and velocity of the

particle at t = 3 s?
Engineering
1 answer:
lidiya [134]3 years ago
6 0

Answer:

v=82 m/s

s=116m

Explanation:

a=20t

\frac{\mathrm{d} v}{\mathrm{d} t}=20t\\\int\limits dv =\int(20t) dt\\v={10}t^2+c

using condition given at t=0

-8=10\times 0^2 +c

c=-8

now equation becomes

v=10t²-8

v at t= 3s  v=82 m/s

again

\frac{\mathrm{d} s}{\mathrm{d} t}=10t^2-8

ds=(10t^2-8)dt\\\int\limits ds =\int(10t^2-8) dt\\s=\frac{10}{3} t^2-8t+b

now using condition given s=50 at t=0

b=50

now equation becomes

s=\frac{10}{3}t^3-8t+50

calculating s at t=3s

s=116m

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