Question

An object is moving along the x-axis. It's x-velocity as a function of time is given by v_x = 3 t² - 2 t (which gives v_x in meters for t in seconds). What is its displacement during the time interval from t = 2 s to t = 4 s?

Answer Choices:

44

60

48

34

12

Answer 1

velocity along the X axis, V_x = 3t² - 2t  

V_x (t =2) = (3 * 2²⁾ - (2 * 2) = 8 m/s = U(initial velocity for the interval t=2 s to t = 4 s)

and V_x (t =4) = (3 * 4²⁾ - (2 * 4) = 40 m/s =V(final velocity for the interval t=2 s to t = 4 s)

acceleration in this interval, a = (V-U)/T ; where T =time interval = (4-2) s = 2 s
= (40-8)/2 m/s²

  = 16 m/s²

displacement during this time interval t[2,4], S = UT + (aT²)/2 = (8 * 2) + (16 * 2²)/2 = 16 + 32 = 48 m

displacement during this time interval t[2,4] is 48 m.