The position of a particle as it moves along an y axis is given by y = (2.0cm)sin(πt/4), with t in second and y in centimeters. a. what is the average velocity of the particle between t = 0 and t = 2.0 s? b. what is the instantaneous velocity of the particle at t = 0, 1.0, and 2.0 s? c. what is the average acceleration of the particle between t = 0 and t = 2.0 s? d. what is the instantaneous acceleration of the particle at t = 0, 1.0, and 2.0 s?

Part a)

At t = 0  the position of the object is given as

At t = 2

so displacement of the object is given as

so average speed is given as

Part b)

instantaneous speed is given by

now at t= 0

at t = 1

at t = 2

Part c)

Average acceleration is given as

Part d)

Now for instantaneous acceleration

As we know that

at t = 0

at t = 1

now we have

At t = 2 we have

so above is the instantaneous accelerations

answer

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explanation:

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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