A rocket-powered hockey puck moves on a horizontal frictionless table, the figur

Question

A rocket-powered hockey puck moves on a horizontal frictionless table, the figure(Figure 1) shows graphs of vx and vy, the x- and y-components of the puck's velocity. The puck starts at the origin. What is the magnitude of the puck's acceleration? Hint: The x-component of the acceleration vector can be found by taking the dv_x/dt: which is the slope of the tangent at any point on a v_x vs t curve. A similar thing can be done to get v_y component. Use usual procedure to get magnitude of vector. Express your answer using two significant figures. How far from the origin is the puck at t = 0s? Express your answer using two significant figures. How far from the origin is the puck at t = 7s? Express your answer using two significant figures. How far from the origin is the puck at t = 9s?

Explanation / Answer

we can get acceleration of particle along x axis is calculated by using graph plotted
is a = v/t = -2mts/sec^2

we can get acceleration of particle along x axis is calculated by using graph plotted
is a = v/t = +1mts/sec^2    

the accelaration of whole particle is a = -2i + 1j in vector form

accealation magnitude is ((2^2) + (1)^2) = (4 + 1) =(5) = 2.24mts/sec^2 (two significant digits)

as the body starts from origin we can say that at tme t = 0 distance from origin is zero

distance of puck from origin after time t is calculated by using s =ut + 1/2at^2

now using the components of accelaration along repective directions

s = (10*7 -1/2*2*(7)^2 )i + (0 +1/2(1)(7^2))j

s = 21i + 24.5j

s = (21^2 +24.4^2) = 32.3mts from origin

substitituting 9 seconds instead of 7 seconds we get s = 9i + 40.5j =

s = (9^2 + 40.5^2) = 41.49 mts from originafter 9 seconds

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