9. Consider the following position vs time functions, i.e. analytical expression

Question

9. Consider the following position vs time functions, i.e. analytical expressions for the position of an object along the x-axis as a function of time. In physics you will learn that given the function for position vs time, one can find the instantaneous velocity of the object by differentiating the x(t) function wir to time, i.e. y(t) = dx/dt Determine the expression for v(t) for each of the following x(t) expressions: xr(t)-5.0 x2(t) = 5.0 t-20 x3(t) = 4.0 t2-3.0 t + 6.0 X4(t) = 5.0 sin(5t) x(t)-2.0 cos(31+2) v2(t)- V3(t) = V4(t) = vs(t) = Now, give numerical values for each of the following: V2(0) = Vs(0) V4(0.2)= ; xs(0)= x3(2)- x4(0.1 ) = vs(0.4) = V2(4) , vs(4)- 10. In physics you will learn that the work done by a force in moving an object from x = a to x-b is given by: Work-jf(x)dx Determine the work for the following force functions for the specified displacement f(x)-5.0 N b=10m work = f(x)- 4.0x b=1.0m 4

Explanation / Answer

We have been given,

v(t)=dx/dt

So we just have to differentiate the given functions of displacement.

v1(t)=0

v2(t)=5

v3(t)=8t-3

v4(t)=25cos(5t)

v5(t)=-6cos(3t+2)

Now, just put the different values of t

v2(0)=5

v3(0)=-3

v4(0.2)=2.7

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