If the position vector of the particle is given by vector r=3t^2i+5tj+4k find the velocity of the particle at t=3secs
speed of the particle at t=3secs
acceleration of the particle at time t=3secs​

Scientists use laser range-finding to measure the distance to the moon with great accuracy. a brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. a laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. in order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0 km in diameter. staying within this diameter is accomplished by using a special large-diameter laser. part a if λ = 540nm , what is the minimum diameter of the circular opening from which the laser beam emerges? the earth-moon distance is 384,000 km. express your answer to two significant figures and include the appropriate units.

The force acting on a beam was measured under the same operating conditions and a sample of 5 data points was collected. this process was repeated by 3 observers. the pooled standard deviations of these 3 data sets was 1.21. determine the true mean force using all pooled data (with a 95% probability). the result should look like this: true mean = mean +/- margin of error

Hey student studies gravity using objects that have the same mass which two objects have the greatest gravitational force acting between them a. 100kg 1.0m 100kg b. 100kg 2.0m 100kg c. 100kg 2.0m 100kg big d. 100kg big 3.0m 100kg big