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- 1. A particle moves along the x axis according to the equation x = 2 +9t - 3t², where x is in meters and t is in seconds. At t = 3.00 s, find .... (a) the position of the particle, (b) its velocity, and (c) its acceleration (10pts)1. Driver A is cruising along enjoying the fall colors. Driver B starts driving her car the instant he passes her. They both drive along a straight line. Their velocities are shown as functions of time in the graph. At what instants in time are drivers A and B side by side? The dotted lines are to guide the eyes. v (m/s) 40 20 1 2 3 Car B 4 Car A 5 6 7 8 9Two kids are racing towards a toy somewhere between them. Albert has 3.90 times further to run than Betty. Albert is to the West of the toy and Betty is to the East of the toy. Albert runs at a constant speed of 1.60 m/s. It takes him 2.90 s to reach the toy.How far did Albert run to reach the toy?
- 7. The height of a helicopter above the ground is given by h =20.0 t-5.0 t where h is in meters and t is in seconds. At t=1.00 s, the helicopter releases a small mailbag. a) What is speed of a mailbox before hint to the ground? b) How long mailbox in air? 8. Starting from rest at 5 m from origin, a small still ball's horizontal component of velocity is 90.0 mile/hour in a straight line in 10.0 s. Ball's acceleration is constant during the entire motion, what is ball's final position?2. A child running around in a field has the following position and velocity at time t = 0: x = 1.5 m, y = 2.0 m Vx = -3.5 m/s, vy=-1.0 m/s At time t = 2.5 s, it has the following position and velocity: x = -2.0 m, y = 1.5 m vx = -0.50 m/s, v, = 2.0 m/s Using this information, find the child's average velocity and average acceleration during that time interval. Write your answers in unit vector notation.3. A bee flies in a straight line (a "beeline" as they say). The initial speed of the bee is Vo = 100 cm/s. The acceleration of the bee versus position is given by the graph below. a [cm/s²] 500 0 -250 50 105 145 195 s [cm] a. At what position will the speed of the bee be maximum? Hint: it will be one of the labeled points: 0cm, 50cm, 105cm, 145cm or 195cm. b. What is the speed of the bee at that location? C. What is the speed of the bee after traveling the full 195cm? Hints: you don't need to figure the equations for the four lines to do the integrals, and be careful of the signs.
- A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 23.0 m/s, and the distance between them is 55.0 m. After t₁ = 3.00 s, the motorcycle starts to accelerate at a rate of 7.00 m/s². The motorcycle catches up with the car at some time t2. Figure 1 of 1 car motorcycle x(1) car x(1) x(1) BRE car motorcycle motorcycle A time с time time motorcycle x(1) car car LE motorcycle B time D time How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words, find t₂ - t₁. Express the time numerically in seconds using three significant figures. ► View Available Hint(s) VE ΑΣΦ ? t₂-t₁= 1.58 Submit Previous Answers X Incorrect; Try Again; 4 attempts remaining Part C How far does the motorcycle travel from the moment it starts to accelerate (at time t₁) until it catches up with the car (at time t₂)? Should you need to use…814. The speed of a nerve impulse in the human body is about 100 m/s. If you accidentally stub you toe in the dark, estimate the time it takes the nerve impulse to travel to your brain. (Assume that you are approximately 1.70 m tall and that the nerve impulse travels at uniform speed.)
- 1. Suppose that the velocity of a particle in motion is given by v(t) = 44t² +²+1 feet per second, where t is in seconds from now. Find the position of the particle after 5 seconds.1. The cheetah can reach a top speed of 114 km/h. while chasing its prey in a short sprint, a cheetah starts from rests and runs 45 min in a straight line, reaching a final speed of 72 km/h. a. Determine the cheetah's average acceleration during the short sprint, and b. Find its displacement at t= 3.5 s O 4.4m/s2, 27m O 5.6m/s2, 56m O 1.2m/s2, 15mA scooter begins at rest at t0=0 seconds. The scooters starts moving, and eventually covers a distance d= 651m, in a time tf= 104 seconds. In a coordinate system with north being the positive x-direction, the scooter's motion is in the northern direction. What wa the scooter's average speed, during this time period, in meters per second? What was the scooters displacement in the northern direction during this person, in meters? What was the scooter's average velocity in the northern direction, in this period in meters per second? If the scooter's final velocity at tf was 12 m/s, what was the scooter's average acceleration in the northern direction, during this period in m/s%^2?