A particle moves in a horizontal line so that its position from a fixed point after t seconds, where t≥ 0, is s metres, where s(t) = 52²2²-A. a Find the position, velocity and acceleration of the particle after 1 second. b Determine whether the particle is speeding up or slowing down at t = 1. c Find the values of t when the particle is at rest. d Find the time intervals on which the particle is speeding up, and the intervals on which it is slowing down. e Find the total distance the particle travels in the first 3 seconds.

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 24

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.

A jet plane lands with a speed of 145 m/s and can accelerate at a maximum rate of -7.00 m/?2 as it comes to rest. a. From the instant the plane touches the runway, what is the minimum time interval needed before it can come to rest? b. Can this plane land on a small tropical island airport where the runway is 0.9 km long? Why?

2. V A particle moves according to the equation ¤ = 10t², where is in meters and t is in seconds. (a) Find the average velocity for the time interval from 2.00 s to 3.00 s. (b) Find the average velocity for the time interval from 2.00 to 2.10 s.

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.

A particle travels along the +x axis. At t = 0 s, its velocity is 10.0 m/s and its acceleration is -2.0 m/s^2.  Question A: Which of the following statements is true?           1. The particle will slow down and eventually come to a complete stop           2. The particle cannot have a negative acceleration and be moving in the positive x direction           3. The particle will continue to move in the positive x direction, slowing but never coming to a complete stop.           4. The particle will slow down, stop momentarily, then speed up in the x- direction.  Question B: At what time will the particle be stopped?           1. t = 5.0 s          2. t = -5.0 s          3. t = -0.2 s          4. The particle does not ever stop  Question C: What is the particle's displacement from its initial position at t = 10.0 s ?  Please Answer questions A, B, and C

Anna and Bridget live 33 km apart. They cycle to meet each other. Anna travels at 10 km/h and Bridget travels at 12 km/h. a  How long until they meet each other? b  What distance have they each travelled?

B A ball is thrown upward with a speed of 40 m/s. Approximately how much time goes it take the ball to travel from the release location (A) to its highest point (B)? Approximately how much total time is the ball in the air before it returns toback to its original height (C)? A Moving from Point A to Moving from Point A to Point B to Point C. Point B. Time (s): Time (s): Tap to Answer Tap to Answer