An object moves along the x axis according to the equation x = 3.50t2 - 2.00t +
ID: 1958792 • Letter: A
Question
An object moves along the x axis according to the equation x = 3.50t2 - 2.00t + 3.00,where x is in meters and t is in seconds.(a) Determine the average speed between t = 2.10 s and t = 4.00 s.________ m/s
(b) Determine the instantaneous speed at t = 2.10 s.________ m/s
Determine the instantaneous speed at t = 4.00 s._______ m/s
(c) Determine the average acceleration between t = 2.10 s and t = 4.00 s._______m/s2
(d) Determine the instantaneous acceleration at t = 2.10 s._____________m/s2
Determine the instantaneous acceleration at t = 4.00 s.________m/s2
(e) At what time is the object at rest?________s
Explanation / Answer
a) the average speed is going to be x(4) - x(2.1)/(4-2.1) = (3.50(4)^2 - 2.00(4) + 3.00) - (3.50(2.1)^2 - 2.00(2.1) + 3.00)/1.9 = 51 - 22.635/1.9 = 28.365/1.9 = 14.93 m/s b) The instantaneous speed is the first derivative of x(t) will be 7(t) - 2, so at time t = 2.1 this is 12.7 m/s and at time t = 4, this is 26 m/s c) average acceleration will be 26-12.7/1.9 = 7 m/s^2 d) the instantaneous acceleration will be the 2nd of x(t) which is simply 7. So at time t=2.1 the acceleration is 7 m/s^2 e) the object is at rest when the speed is zero or when 7(t) - 2 = 0. Solve this for t 7(t) - 2 = 0 7(t) = 2 t = 2/7 s