Question

Speed means the absolute value of the velocity, hence it is always non-negative. While the sign of the velocity indicates the direction of the motion, the speed is insensitive to the direction. For example, speed is the value displayed by car’s speedometer; it does not indicate the direction of driving (e.g., northbound versus southbound). At time t = 0 seconds (s) an object has zero velocity and it starts a free fall from the altitude of 1200 metres (m) above Earth’s surface. We assume that the air resistance is negligible and the gravitational acceleration is −9.81 m/s 2 . At the time instant when the object is falling with the speed of 50 m/s, its brake engines are ignited and from then on, the object is moving vertically with a constant acceleration of 1 m/s 2 until it hits the ground. (Note the sign of the acceleration: the breaking force is stronger than the gravitational force.)

(a) Determine two position functions: yf (t) for the free fall motion and yb(T) for the motion with brakes ignited. The new time variable T is such that T = 0 is the time when the brakes are ignited.

(b) Determine the time when the object hits the ground and the speed at which it hits the ground. Express the hitting time in terms of t (total travel time)

Answer 1