2. 1D Motion / Kinematics

Suppose a cart moves along a straight track and its position as a function of time is given by $x=2t+3$. Which graph best represents the velocity of the cart as a function of time?

In a $\mathrm{position}$ vs. $\mathrm{time}$ graph, what information is typically presented on the y-axis?

Which of the following sets of motion graphs is consistent for an object moving with constant positive $a$?

Draw position, velocity, and acceleration graphs for the ball shown in FIGURE P2.44. See Problem 43 for more information.

(II) The position of a race car, which starts from rest at t = 0 and moves in a straight line, is given as a function of time in the following Table. Estimate its acceleration as a function of time. Display each in a Table and on a graph.

A police car at rest is passed by a speeder traveling at a constant 140 km/h. The police officer takes off in hot pursuit and catches up to the speeder in 850 m, maintaining a constant acceleration. Qualitatively plot the position vs. time graph for both cars from the police car's start to the catch-up point.

The position of a small object is given by 𝓍 = 27 + 10t - 2t³, where t is in seconds and 𝓍 in meters. Plot 𝓍 as a function of t from t = 0 to t = 3.0 s.

In a graph depicting motion, how would you identify the independent variable?

Ann and Carol are driving their cars along the same straight road. Carol is located at x = 2.4 mi at t = 0 h and drives at a steady 36 mph. Ann, who is traveling in the same direction, is located at x = 0.0 mi at t = 0.50 h and drives at a steady 50 mph. Draw a position-versus-time graph showing the motion of both Ann and Carol.

Which of the following sets of graphs is consistent with an object moving with constant positive acceleration?

(II) The position of a race car, which starts from rest at t = 0 and moves in a straight line, is given as a function of time in the following Table. Estimate its velocity as a function of time. Display each in a Table and on a graph.

A police car at rest is passed by a speeder traveling at a constant 140 km/h. The police officer takes off in hot pursuit and catches up to the speeder in 850 m, maintaining a constant acceleration.

(a) Qualitatively plot the position vs. time graph for both cars from the police car's start to the catch-up point.

Calculate (b) how long it took the police officer to overtake the speeder,

FIGURE P1.58 shows a motion diagram of a car traveling down a street. The camera took one frame every 10 s. A distance scale is provided. Make a position-versus-time graph for the car. Because you have data only at certain instants of time, your graph should consist of dots that are not connected together.