t 2 )2, where b 7.00 m,-2.00 m/s2, and x may be from the will be in meters when
ID: 1575924 • Letter: T
Question
t 2 )2, where b 7.00 m,-2.00 m/s2, and x may be from the will be in meters when t is in seconds. Determine the following. (Where applicable, indicated direction with the sign of your answer.) (a) position, velocity, and speed of the particle at the time t-os (Enter your answers to at least one decimal place.) position xtt O s) velocity vit- 0s)- speed v(t-0 s) " (Enter your answels to at least one decimal place.) (b) position, velocity, and speed of the particle at the time t- 4 s position x(t 4s) velocity t-4s) - speed v(t 4s) - (e) time and position of the particle when it changes direction (Enter your answers to at least one decimal place.) xtt- Ichange) - (d) displacement, distance traveled, average velocity, and average speed of the particle over thetim e interval t 4 s change distance d(t-0 4 s) " average velocity v(t-0 s)- average speed vet-0 4 s)- m/sExplanation / Answer
a)
x(t) = 7 + 2 (t - 2)2
at t = 0
x(0) = 7 + 2 (0 - 2)2 = 15 m
velocity is given as
v(t) = dx(t)/dt = 4 (t - 2)
at t = 0
v(0) = 4 (0 - 2) = - 8 m/s
speed = 8 m/s
b)
x(t) = 7 + 2 (t - 2)2
at t = 4
x(4) = 7 + 2 (4 - 2)2 = 15 m
velocity is given as
v(t) = dx(t)/dt = 4 (t - 2)
at t = 4
v(4) = 4 (4 - 2) = 8 m/s
speed = 8 m/s
c)
velocity is given as
v(t) = 4 (t - 2)
while changing direction
v(t) = 0
4 (t - 2) = 0
t = 2
x(t) = 7 + 2 (t - 2)2
at t = 2
x(2) = 7 + 2 (2 - 2)2 = 7 m
d)
displacement = x(4) - x(0) = 15 - 15 = 0 m
distance travelled = 15 + 15 = 30 m
average velocity = displacement /time = 0 m/s
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