The aceleration of the particle is given by a=2.0sqrt t. At t=0, v=7.5m/s and x=0. what...

Question

Question

The aceleration of the particle is given by a=2.0sqrt t. At t=0, v=7.5m/s and x=0.

what is the speed as a function of time? what is the displacementas a function of time?

what are the aceleration , speed and displacement at t=5.0s?

science physics

Answer 1

Answer #1

a = 2 sqrt(t)

dv = a.dt = 2 sqrt(t) dt

integrating both sides,

v - v0 = 1 / sqrt(t)

v - 7.5 = (1/ sqrt(t))

v = 7.5 + (1/sqrt(t)) ........Ans

dx = v.dt = (7.5 + (1/sqrt(t))) dt

integrating,

x = 7.5t - 0.5(t)^-1.5 .......Ans

at t= 5 sec

a = 2 sqrt(5) = 4.47 m/s^2

v = 7.5 + (1/sqrt(5)) = 7.95 m/s

x = (7.5 * 5) - (0.5 * 5^1.5) = 37,46 m

Answer 2

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