A body moving with uniform acceleration Travels 84 metre in the first 6 second and 180 m in the next 5 seconds. find: (a) the initial velocity ,and (b) the acceleration of the body ?

1 Answer
MattyMatty
Jun 10, 2018

#"a) initial velocity "v_0 = 2 m/s#
#"b) acceleration "a = 4 m/s^2#

Explanation:

#x = v_0 * t + a * t^2 / 2#

#"Here we have"#

#84 = 6 v_0 + 18 a#
#84 + 180 = 264 = 11 v_0 + 60.5 a#

#"This is a linear system of two equations in the variables "v_0#
#"and "a.#

#=> 14 = v_0 + 3 a" (Equation 1 divided by 6)"#
#=> v_0 = 14 - 3 a#
#=> 264 = 154 - 33 a + 60.5 a" (Eq. 2 with "v_0" replaced)"#
#=> 110 = 27.5 a#
#=> a = 110 / 27.5#
#=> a = 4#
#=> v_0 = 14 - 3*4 = 2#

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