The motion of a dog is observed to be given by the function r = (1.9 m/s²) t²i-[(0.7 m/s³) t³-2.9 mlj. What is the magnitude of the instantaneous velocity of the dog between t=0 and t=3.07 s? O 8.12 m/s O 7.48 m/s 24.94 m/s O 22.97 m/s

A space shuttle is fired and the position of the shuttle is given by r(t)=(2*t*t-5*t)i+ (3*t+1)j+(12*t*t*t)k where t is in seconds, r is in meters and ij,k are the unit vectors of x,y,z directions respectively. Find the average acceleration of the space shuttle between the time interval t=10 s and t=1 minutes. *

A badger looking for food travels 8.0 km [S], 3.0 km [E], 5.0 km [S], 9.0 km [N], then 3.0 km [W]. What is the badger's total displacement?

At the beginning of a 3 hour trip you're traveling due north at 192 km/hour. at the end, you are traveling 240km/hour at 45° west of north. a) Draw the initial and final velocity vectors   b) find Δv

1. The motions of two objects, A and B, are defined by the following vectors: vector A = 6.0622i + 3.500j m/s vector B = 5.9500i + 10.3057j m/s unit vector of bullet = -j After 20s, what is the total distance travelled by object A?

A fast food restaurant uses a conveyor belt to send the burgers through a grilling machine. If the grilling machine is 1.1m long and the burgers require 2.5min to cook, how fast must the conveyor belt travel? If the burgers spaced 15cm apart, what is the rate of burger production (in burgers/min)?

We choose a reference system with the positive x-axis in the eastward direction and the positive y-axis vertically upward. In this frame of reference, vCE = 45.0 km/h in the positive x-direction, and VRE = Vrain in the negative y-direction. For the velocity components of the car and rain relative to the Earth, we have (V ce)x = +([ (VRE)x = 0, ] km/h), cely = 0 (VREly = -Vrain Therefore, for the x-component of velocity of the rain relative to the car, we have (VRc)x = 0 - ] km/h) = - (| ] km/h). and for the y-component of velocity of the rain relative to the car, = -Vrain- 0 = -Vrain %3D

(a) A soccer player kicks a rock horizontally off a 39 m high cliff into a pool of water. If the player hears the sound of the splash 3.02 s later, what was the initial speed given to the rock (in m/s)? Assume the speed of sound in air is 343 m/s. m/s (b) What If? If the temperature near the cliff suddenly falls to 0°C, reducing the speed of sound to 331 m/s, what would the initial speed of the rock have to be (in m/s) for the soccer player to hear the sound of the splash 3.02 s after kicking the rock? m/s

A train composed of a small engine car and a massive cargo car are connected as they move along a track. The speed of the small engine car is ____(blank 1)___ the speed of the massive cargo car. The magnitude of the acceleration of the small engine car is ____(blank 2)___ the magnitude of the acceleration of the massive cargo car because ____(blank 3)___ .