The speed of an object traveling along the x axis increases at the constant rate

Question

The speed of an object traveling along the x axis increases at the constant rate of 4.6 m/s each second. At t = 0.0 s, its velocity is 1.2 m/s and its position is +7.0 m. (a) How fast is it moving when its position is 8.0 m? _______ m/s (b) At this point, how much time has elapsed from the start at t = 0.0 s? _______ s A ball is launched directly upward from ground level with an initial speed of 16 m/s. (Air resistance is negligible.) (a) How long is the ball in the air? 3.26 s (b) What is the greatest height reached by the ball? 13 m (c) How many seconds after launch is the ball 7 m above the release point? _______ s after being thrown (first time) _______ s after being thrown (second time)

Explanation / Answer

a = 4.6 m/s^2

v0 = 1.2 m/s

x0 = 7 m

(A) xf = 8 m

displacement, x = xf -x0 = 1 m

Applying vf^2 - vi^2 = 2 a x

v^2 - 1.2^2 = 2 x 4.6 x 1

v = 3.26 m/s ........Ans

(b) v = v0 + at

3.26 = 1.2 + 4.6 t

t = 0.45 sec

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3. (c) v0 = 16 m/s

Applying d = v0 t + a t^2 /2

7 = 16 t - 9.8 t^2 / 2

4.9 t^2 - 16 t + 7 = 0

t = 0.52 sec Or 2.74 sec

  

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