## Evenly Varied Movement

**1.** During a car race, one of the competitors can reach 100km / h from the start in 5s. What is the average acceleration he describes?

**2. **A piece of furniture, starting from rest with a constant acceleration equal to 1m / s² moves for 5 minutes. At the end of this time, how fast is it acquired?

**3. ** A car is standing in front of a traffic light. As soon as the signal opens, it starts with 5m / s² acceleration, meanwhile a truck passes by with a constant speed of 10m / s.

(a) After how long does the car reach the truck?

(b) What is the distance traveled to the meeting.

*The equations of muv for the car and mu for the truck are written:*

*Car: *

*Truck:*

*When the two meet, their positions are equal, so:*

*(b) Knowing the moment of the meeting, it is only necessary to apply it in one of two functions (truck or car).*

*Soon the car meets the truck 4 seconds after the traffic light opens, at a distance of 40 m.*

**4. **A motorcycle travels at a constant speed of 30m / s. When the rider sees a person cross the road, he brakes the bike to a stop. Knowing that the maximum acceleration for braking the motorcycle has an absolute value of 8m / s², and that the person is 50m away from the motorcycle. Will the rider be able to fully brake the motorcycle before reaching the person?

*As the acceleration used to brake the motorcycle opposes the movement, has negative value, so:*

*The motorcycle will not stop before hitting the person.*

**5.** A runner reaches the finish line in a race with a speed of 18m / s. Upon arrival he walks another 6 meters until he stops completely. What is the value of your acceleration?

## Vertical movement

**1.** A rock is abandoned from a 100m high cliff. How fast does it get to the ground? How long does it take to arrive?

**2. **In a game called "Stop" the player must throw the ball vertically upwards and shout the name of someone who is in the game. When the ball returns to the ground, the called player must hold the ball and shout: "Stop", and all others must stop, so the called person must "hunt" the other players. When one of the children throws the ball up, it reaches a height of 15 meters. And returns to the ground in 6 seconds. What is the initial launch speed?

*To perform this calculation one must divide the movement into rise and fall, but we know that the time taken for the ball to return is twice the time it spends up or down. So:*

*Rise (t = 3s)*

**3.** While shooting a movie, a stuntman must fall off a 30m high cliff and fall onto a mattress. When it reaches the mattress, it undergoes a deformation of 1m. What is the slowdown that the stuntman suffers until he stops when he gets a mattress?

*The deceleration suffered by the stuntman will occur when the initial velocity is the vertical ground velocity, the final velocity is zero, and the displacement distance is 1m deformation of the mattress. So the first step to reaching resolution is figuring out the ground speed:*

*Since exercise is not given time, the fastest way to calculate velocity is through the Torricelli Equation for vertical motion with positive gravity acceleration, since motion is in the same direction as gravity.*

*The second step is **calculate the uniformly varied motion for the deceleration of the fall. With initial speed equal to 24,5m / s.*

**4. **A farmer needs to know the depth of a well on his land. Then he leaves a rock in the well's mouth and times the time it takes to hear the sound of the rock in the background. He notes that the timed time is 5 seconds. How high is the well?

*We can divide the moving motion of the stone and the displacement of sound.*

*Stone Movement:*

*Sound Shift:*

*Knowing that the well height is the same for both functions and that *:

but , then:

Knowing that

Taking the times of each movement, we can calculate the height using either of two functions: