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Interactive Exercises 2.14: Acceleration and Velocity Plots (Monster RC Truck) A radio-controlled (RC) truck moves along an x axis with an acceleration that depends on time in a manner shown in the graph in Interactive Fig. 2.14.1 below. At the instant0 the velocity of the truck is -1 m/s and its position is at the origin a (m/s) 0, 1 (s) 10 Interactive Figure 2.14.1: The acceleration versus time plot for an RC truck that moves on an axis.

▼ Question 1 What is the velocity ofthe truck at t = 10 s? Enter a numerical value in the box below m/s the tolerance is +/-2% By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set by your instructor Attempts: o of 5 used SAVE FOR LATER SUBMIT ANSWER SUBMIT ANSWER Question 2 Find an expression for the velocity v(t) of the truck at any instant t in the interval 0 St exponents in the last box 5 s. Enter numerical values in the first and the third boxes, units in the second and the fourth boxes, and v(1) = By accessing this Question Assistance, you will learn while you earn points based on the Point Potential Policy set by your instructor. Attempts: o of 5 used SAVEPORTER SUBMIT ANSWER SUBMIT ANSWER

Question 3 Next, consider the case where 5 10 s, which is on the downward sloping portion of the acceleration plot. The case is depicted in Interactive Fig. 2.14.4 below. The trucks velocity change is the sum of the areas of the blue triangle, the tan rectangle, and the green triangle. We can use this graph to derive an expression for v(t) for 5 sts10 s What is this area? this line segment: 1-0.1r equation of this line segment: 0.1 a (m/s) 10 What is this area? What is this area? Interactive Figure 2.14.4: An arbitrary instant t >5 s is shown. The total of the areas of the blue triangle, the tan rectangle, and the green triangle gives the velocity change for the interval from t 0 to

We are now in a position to plot the velocity of the truck as a function of time over the ten-second time interval of interest, as shown in the figure below. The answer to question 2 is used for the velocity in the time interval O t< 5 s, and Eq. (A) is used for the velocity in the time interval 5 s St 10 s. v (m/s) 1.0 r (s) 0.5 Interactive Figure 2.14.5: Velocity versus time of RC truck based on finding area under plot of acceleration versus time Since the trucks initial velocity is a negative number, and the acceleration is positive for 0<t< 10 s, you should expect the truck to slow down initially, stop for an instant, and then speed up while moving in the +x direction. This is exactly what the velocity versus time plot tells us happens! At what instant will the truck have its most negative position? Enter a numerical value in the box below the tolerance is +/-296

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