An object moves along the x axis according to the equation x = 3.50t2 - 2.00t +
ID: 1310600 • 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 = 3.30 s.
????? m/s
(b) Determine the instantaneous speed at t = 2.10 s.
????? m/s
Determine the instantaneous speed at t = 3.30 s.
????? m/s
(c) Determine the average acceleration between t = 2.10 s and t = 3.30 s.
????? m/s2
(d) Determine the instantaneous acceleration at t = 2.10 s.
????? m/s2
Determine the instantaneous acceleration at t = 3.30 s.
????? m/s2
(e) At what time is the object at rest?
????? s
Explanation / Answer
a). avg.speed= total distance/total time
at t=3.30, distance=34.51 at t=2.10, distance=14.23
avg.speed=20.28/1.2
=16.9
b). first derivative of x= 7t-2
instantaneous speed at t = 2.10s is, 7(2.1)-2= 12.7
instantaneous speed at t = 3.30 s is 21.1
c). avg.accelaration= Change in velocity / time interval
=21.1-12.7/1.2
=7
d).instantaneous acceleration at t = 2.10 s. i.e 8.4/2.1 =4
instantaneous acceleration at t = 3.30 s i.e 8.4/3.3= 2.54
e). 0.28s