Answer to Question #104565 in Mechanics | Relativity for Prince

Question #104565
An object has a constant acceleration a=4m/s². It's velocity is 1m/s at t=0, when it is at x=7m. How fast is it moving when it is at x=8m? At what time is this?
1
Expert's answer
2020-03-05T09:34:15-0500

"a=4\\ m\/s^2"

"v_i=1\\ m\/s, \\ \\ x_i=7\\ m" , "t=0 \\ s"

"v_f \\ - ?, \\ x_f=8\\ m" , "t - ?"


Solution:

Using formula "v_f^2=v_i^2 +2ad, (d" - displacement")" we have:

"v_f^2=1^2+2\\times 4\\times (8-7)=9, \\; \\; v_f=3\\ m\/s"

To find time (when "v_f=3\\ m\/s" ) we can use formula for velocity of object with constant acceleration:

"v_f=v_i+at,"

"t=\\frac{v_f-v_i}{a}=\\frac{3-1}{4}=0.5 \\ s"

Answer: "v_f=3 \\ m\/s, \\; t=0.5\\ s."



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