A car traveling at a constant speed of 55.0 m/s passes a trooper on a motorcycle hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets out from the billboard to catch the car, accelerating at a constant rate of 2.00 m/s². How long does it take the trooper to overtake the car? Solve this problem by a graphical method. On the same graph plot position versus time for the car (solid black line) and the trooper (dashed blue line).

A coordinate plane has a horizontal axis labeled t (s) and a vertical axis labeled x (km). There are two curves.

• The first, solid line begins just above the origin, moves up and to the right in a straight line, and exits the viewing window at approximately (62,3.4).
• The second, dashed line is nearly horizontal when it enters the viewing field at the origin, then curves upward and to the right with increasing slope until it exits the viewing window at approximately (62,3.8).

A coordinate plane has a horizontal axis labeled t (s) and a vertical axis labeled x (km). There are two curves.

• The first, solid line enters the viewing field at x = 3.7, moves down and to the right in a straight line, and exits the viewing field just above x = 0.
• The second, dashed line is nearly horizontal when it enters the viewing field at the origin, then curves upward and to the right with increasing slope until it exits the viewing window at approximately (62,3.8).

A coordinate plane has a horizontal axis labeled t (s) and a vertical axis labeled x (km). There are two curves.

• The first, solid line begins just above the origin, moves up and to the right in a straight line, and exits the viewing window at approximately (62,3.4).
• The second, dashed line is nearly horizontal when it enters the viewing field at x = 4, then curves downward and to the right with decreasing slope until it exits the viewing window at approximately (62,0).

A coordinate plane has a horizontal axis labeled t (s) and a vertical axis labeled x (km). There are two curves.

• The first, solid line enters the viewing field at x = 3.7, moves down and to the right in a straight line, and exits the viewing field just above x = 0.
• The second, dashed line is nearly horizontal when it enters the viewing field at x = 3.8, then curves downward and to the right with decreasing slope until it exits the viewing window at approximately (62,0).

From the intersection of the two curves read the time (in s) at which the trooper overtakes the car.

s