Activity 1.3 - Graphs of One Dimensional Motion1. Use the data for the cart in the One-Dimensional Motion activity 1.2 to make graphs of the x position vs.time, x-velocity vs. time and x-acceleration vs. time. Draw a line through the data if it falls on a straightline.x (cm)5040302010▼x-position vs. timet=1sA00 0.5 1 1.5 2 2.5 3time (sec)a. At what time is the x-position thelargest?b. What is the x velocity at the timewhen the x-position the largest?c. What is the x-acceleration when the x-velocity is zero?d. What is the value of the slope of the x-velocity vequation you use symbolically, then substitute iyour calculation. Label your answer.x velocity (cm/s)x acceleration (cm/s²)604020-200-40-606040200-20-40-600x-velocity vs. time0.5 1 1.5 2time (sec)0 0.5x-acceleration vs. time12.51.5 2 2.5time (sec)3 e. What quantity does the slope of the x-velocity versus time graph correspond to?f. What quantity does the slope of the x-position vs. time graph correspond to?g. If the x-acceleration is constant than the x-position vs. time is given by1x(t) = x₂ +₁+₁²Here x, is the x-position at t = 0, is the x-velocity at t = 0 and is the constant x-acceleration.Use the graphs on the previous page to identify x V and a for the cart. Write answers belowincluding units. Hint: Vaz is not 30 cm/s. Label your answers, i.e. x₂ =--= -₁0₂ = ₂h. Write an expression for the position as a function of time t for the motion of the cart by substitutingthe correct numerical values (with units) for X Vazand a Start by writing your expressionsymbolically before substituting in the appropriate values (with units) for the constant coefficientsYour final expression should be labeled, x(t) = ---, and should only have numerical values (withunits) and the variablet.i.Substitute t = 0.5 s into the expression you wrote above and check that it agrees with the value x att = 0.5 s on the x vs. t graph. Show the numbers you use in your calculation and check the units arecorrect.j. For constant x-acceleration, the x-velocity as a function of time is given byv₂(t) = V₁z+atWrite an expression for the x-velocity as a function of time t for the cart by substituting the correctnumerical values (with units) for vand a Start by writing your expression symbolically beforesubstituting in the appropriate values (with units) for the constant coefficients. Your final expressionshould be labeled, v. (t) = ., and only have numerical values (with units) and the variablet.

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Use the data for the cart in the One-Dimensional Motion activity 1.2 to make graphs of the x position vs. time, x-velocity vs. time and x-acceleration vs. time. Draw a line through the data if it falls on a straight line.