(A) Find the slope of the velocity vs. time plot. For each second of time that p

Question

(A) Find the slope of the velocity vs. time plot. For each second of time that passes, the velocity gains another 1.6 m/s. The rise in the velocity vs. time plot (the amount by which it increases) divided by the run (the number of seconds that have passed), which gives the slope, is a constant value of 1.6 m/s per second. Therefore, the curve is a straight line with a constant slope of __?__ m/s2 which starts at the initial value vxi = 2.0 m/s.

(B) Find the slope of the distance vs. time plot. A similar principle applies to the displacement. The velocity at t = 4 s is v = vix+ at = m/s. This means that the displacement at that moment is increasing at __?__ m/s, which is the slope of the distance vs. time plot at that instant. But in this case the velocity at each given instant is itself increasing, so that the plot of distance vs. time bends upward.

Explanation / Answer

(a) change in speed per second= 1.6 m/s/s

slope= acceleration= increase in velocity/time

so slope= 1.6 m/s / 1 s

slope= 1.6 m/s^2

(b) V= Vix + a t

a= slope of velocity time graph= 1.6 m/s^2

V= 2 + 1.6(4)

v=2 + 6.4

v= 8.4 m/s

so displacement at that moment is increasing at 8.4 m/s

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