Please answer all parts of quesiton. Thank You A student has acquired data on th

Question

Please answer all parts of quesiton. Thank You

A student has acquired data on the motion of a cart, and created the following mathematical model of the data x(t) 2t +4 I've omitted the units, but it's the usual SI units of meters, seconds, etc. Based on this model, ·Where is the cart at t = 0? How fast is going at t 0? Which way is it going at t-0? What is its acceleration at t= 0? . Can this model be used to tell where the cart is at t 2 s? If so, explain how would you do it. (I'm not asking you to do it, just to explain how you would do it.) If not, explain why not. Can this model be used to tell what the acceleration of the cart is at t 2 s? If so, explain how would you do it. (I'm not asking you to do it, just to explain how you would do it.) If not, explain why not. Can this model be used to tell what the velocity of the cart is at t 2 s? If so, explain how would you do it. (I'm not asking you to do it, just to explain how you would do it.) If not, explain why not.

Explanation / Answer

x = 2t + 4

a) at t=0

x = 2(0) + 4 = 4

x = 4 m

b) we know that

v = dx/dt = d (2t+4)/dt

v = 2 m/s

v is constant with time

at t =0 v = 2 m/s

c) as x is +ve for all t ( +ve) values so it is goinfg in +x direction

d) we know that

a = dv/dt = d(2)/dt

a = 0 m/s2

acceleration = 0

e) as we have the position equaton of cart which is changing with time so we can tell where is cart at t = 2 sec

f) as we know that a = dv/dt

and v = dx/dt

and we have x

so by finding v in form of time we can find a

g) yes

we know that change in position with respect to time is velocity

so we can find velocity at any time.

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