The position of a particle moving along the z-axis is given by a(t) = 6.0 - 2.0t m. Help on how to format answers: units. a. At what time does the particle cross the origin? Answer: b. What is the displacement of the particle between t = 2.0s and t = 4.0 s? Answer:
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- 1. An object's position as a function of time in the x-direction is given by; x(t) : 10 +5e-0.3t (Assume constants have proper SI Units). (E+1)One afternoon, a student was going home after attending a calculus class. For this reason, the student orders an online motorcycle taxi through the application. At the time of ordering, the online motorcycle taxi is in the position s = 2t² + 2t+4, where t is in units of time and s is in meters. a. Determine the average speed of the online motorcycle taxi at intervals of 3 minutes to 5 minutes. b. Determine the time when the instantaneous speed of the online motorcycle taxi is exactly the same as the average speed. NEED IN RUSH THANKSHand written solutions are strictly prohibited.
- A particle P starts at time t = 0 s at the polar position x = -15 m y = 8 m. The velocity of the particle is written in the polar basis associated with its current position, and is: v = 2ê, m/s. If we have final and final, then we can find final and final with: X final symbolic expression X = ? m, yfinal ? Give your answers in symbolic form. You should use the scalar variables r_f and theta_f. Functions are available like sin(), cos(), atan2(), sqrt(), and log(), as well as the mathematical constants pi and e. The regular arithmetic operators are +, -, *, and /, and x^y means x to the power of y. 5t + k would translate to 5*t+k. Now, find the final Cartesian position of the particle at time t = 2. symbolic expression m, y = ? m mAt time t, the position of a body moving along the s-axis is s=−t^3+12t^2−36t m. a. Find the body's acceleration each time the velocity is zero. b. Find the body's speed each time the acceleration is zero. c. Find the total distance traveled by the body from t=0 to t=3.9 ΔΔΔ Δ Δ ΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΔΑ What is the approximate total displacement based on the graph below? use 2 sfs. Approximate the values on each axis to the best of your ability. 560 (velocity mis 50 2240 30 P 10 123 I 3 4 5 Time (s) 1 678 9 2
- A cyclist rides down a long straight road at a velocity (in m/min) given by v(t) = 400 - 20t, for 0≤t≤ 10. a. How far does the cyclist travel in the first 3 min? b. How far does the cyclist travel in the first 10 min? c. How far has the cyclist traveled when his velocity is 350 m/min?4. A robotic vehicle is exploring the surface of Mars. The robot, which is represented as a point, has x - and y-coordinates that vary with time: x = (3 − 2t); y = (-t² + 4t³) where x and y are in meters and t is in seconds. a. Find the average velocity of the robot between t = 0s and t = 2s. b. Find the average acceleration of the robot between t = 0s and t = 2s. c. At what time the acceleration of the robot will be zero. a. Vavg= -21 + 14ĵ m/s b. davg = 22ĵ C. m s² 2 t = = = 0.083 s 24Include a picture or description of your coordinate system (origin, positive direction).
- 1. The acceleration of a car is given by a(t) = A – Bt + Ct² , where A = 1.0 m/s², B = 0.5 m/s³, C = 2.0 m/s“. The car is at rest at the origin at time t= 0. Find its position and velocity as a function of time. b. Sketch its position, velocity, and acceleration. a.The Beretta Model 92S (the standard-issue U.S. army pistol) has a barrel 127 mmmm long. The bullets leave this barrel with a muzzle velocity of 349 m/sm/s. 1) What is the acceleration of the bullet while it is in the barrel, assuming it to be constant? Express your answer in meters per second squared. 2) What is the acceleration of the bullet while it is in the barrel, assuming it to be constant? Express your answer as a multiple of acceleration due to gravity g. 3) For how long is the bullet in the barrel? Express your answer in seconds.At 10:17 a.m., you pass a police car at 55 mph that is stopped on the freeway. You pass a second police car at 55 mph at 10:53 a.m., which is located 39 mi from the first police car. If the speed limit is 60 mph, can the police cite you for speeding? а. a. The total time between your two police car sightings was P hours. b. Your average speed between the two police car sightings was 8, mph. c. Can the police cite you for speeding? No, your average speed was less than the speed limit. CYes, since your average speed was more than the speed limit, there must have been somewhere within the 39 mi where you were driving more than 60 mph.