A vehicle travelling with a uniform velocity was given a uniform acceleration, and in the sixth and tenth seconds after the acceleration began it was observed to travel 15 m and 23 m respectively. What is the acceleration and the initial uniform velocity?

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Answer 1 · 2018-02-17T08:10:39

#a=2" m/s"^2""#

#u=4" m/s"#

I cannot delete my own question but I figured it out. #:.# I shall answer it.

Using the formula below I shall derive two equations and then solve them simultaneously via substitution

#s=ut+1/2at^2#

First, the distance travelled in 6 seconds minus the distance travelled in 5 seconds equals the distance travelled in the sixth second

#15=(6u+1/2a(6^2))-(5u+1/2a(5^2))rArr15=u+(11a)/2#

#rArru=15-(11a)/2# (1)

Second, the distance travelled in 10 seconds minus the distance travelled in 9 seconds equals the distance travelled in the tenth second

#23=(10u+1/2a(10^2))-(9u+1/2a(9^2))rArr23=u+(19a)/2# (2)

Substitute (1) into (2)

#23=15-(11a)/2+(19a)/2rArr8=4arArra=2" m/s"^2""#

#u=15-(11a)/2rArru=4" m/s"#