An object moves along the x axis according to the equation x = 2.55t2 ? 2.00t +
ID: 2282095 • Letter: A
Question
An object moves along the x axis according to the equation x = 2.55t2 ? 2.00t + 3.00, where x is in meters and t is in seconds. (a) Determine the average speed between t = 1.50 s and t = 2.90 s. Correct: Your answer is correct. m/s (b) Determine the instantaneous speed at t = 1.50 s. m/s Determine the instantaneous speed at t = 2.90 s. m/s (c) Determine the average acceleration between t = 1.50 s and t = 2.90 s. m/s2 (d) Determine the instantaneous acceleration at t = 1.50 s. m/s2 Determine the instantaneous acceleration at t = 2.90 s. m/s2 (e) At what time is the object at rest? s
Explanation / Answer
a)
Average Velocity
Vave=dX/dt =[X(t=2.9)-X(t=1.5)]/(t2-t1)]
Vave=[2.55*2.92-2*2.9+3-2.55*1.52+2*1.5-3]/[2.9-1.5]
Vave=9.22 m/s
b)
V(t)=5.1t-2
Instantaneous Velocity
at t=1.5=>V=5.1*1.5-2=5.65 m/s
at t=2.9 s=>V=5.1*2.9-2=12.79 m/s
c)
a=dV/dt =12.79-5.65/(2.9-1.5)
a=5.1 m/s2
d)
acceleration
a=dV/dt= 5.1 m/s2
Instantaneous Velocity
a(t=1.5)=5.1 m/s2
a(t=2.9)=5.1 m/s2
e)
The object is rest at V=dX/dt=0
5.1t-2=0
t=0.392 s