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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/s

Explanation / 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