An object moves along the x axis according to the equation x(t) = (3.30t2 - 2.00
ID: 1961463 • Letter: A
Question
An object moves along the x axis according to the equation x(t) = (3.30t2 - 2.00t + 3.00) m, where t is in seconds.(a) Determine the average speed between t = 1.80 s and t = 3.60 s.
d) Determine the instantaneous acceleration at t = 1.80 s and t = 3.60 s.
Explanation / Answer
a ) Avg speed ( x2 - x1 ) / ( t2 - t1 ) => x1 = x(t1) => x2 = x(t2) b) Take the derivative of x(t) and both time values. This gives you v(t) c) avg acc = ( v2 - v1 ) / ( t2 - t1 ) then find v1 and v2 similarly as for x1 and x2 above. d) Take the derivative of v(t) and plug in your time values. a) x1 = 3.3(1.8^2)-2(1.8)+3 = 10.092 x2 = 3.3(3.6^2)-2(3.6) +3 = 38.568 speed = x2-x1/(t2-t1) = 38.568 - 10.092 /(3.6-1.8) = 15.82 m/s b) x(t) = 3.30t2 - 2.00t + 3.00 v(t) = dx/dt = 6.6t -2 v1 = 6.6(1.8) -2 = 9.88 v2 = 6.6(3.6) -2 = 21.76 acceleration = v2-v1/(t2-t1) = 21.76 - 9.88 /(3.6 -1.8) = 6.6 m/s^2