A tourist drives 90 miles along a scenic highway and then takes a 5-mile walk along a hiking trail. The average velocity driving is nine times that while hiking. Express the total time for driving and hiking, T, as a function of the average velocity on the hike, x.

Peacock mantis shrimps (Odontodactylus scyllarus) feed largely on snails. They shatter the shells of their prey by delivering a sharp blow with their front legs, which have been observed to reach a peak speed of 23 m/s. What is this speed in kilometers per hour?

After an​ accident, police can estimate the speed that a car was traveling by measuring its skid marks. The formula v=2 √5L can be used where v is the​ speed, in miles per​ hour, and L is the length of the skid​ marks, in feet.   ​(a) Estimate the speed of a car that left skid marks 180 ft long. ​(b) If the posted speed limit is 50 mph should the police officer believe the​ driver's claim that he was not​ speeding?

The acceleration of a particle is a constant. At t=0 the velocity of the particle is (14.91 + 18.4ĵ) m/s. At t = 4.6 s the velocity is 11.4j m/s. (Use the following as necessary: t. Do not include units in your answers.) (a) What is the particle's acceleration (in m/s²)? = î+ 18.4 v(t) = (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin. r(t) = î+ X Î- i) m/s m/s

The acceleration of an object (in m/s2) is given by the function a(t)=8sin(t)a(t)=8sin(t). The initial velocity of the object is v(0)=−10v(0)=-10 m/s. Round your answers to four decimal places.a) Find an equation v(t) for the object velocity.v(t)v(t) = −8cos(t)−2Correct  b) Find the object's displacement (in meters) from time 0 to time 3.3.4187Incorrect   metersc) Find the total distance traveled by the object from time 0 to time 3.   meters

Speedometer readings for a vehicle (in motion) at 13-second intervals are given in the table. t (sec) v (ft/s) 28 13 21 26 24 39 19 52 26 65 18 Estimate the distance traveled by the vehicle during this 65-second period using the velocities at the beginning of the time intervals. We can do this by approximating the area under a curve. But what curve? In this case, imagine that the velocity of the vehicle is a function of time, v(t). We do not have this function, but we do have the values of th function at certain points in time. If we assume the function (the velocity) is constant between these points in time (which is not actually true), we can get an approximation. distance traveled - feet Give another estimate using the velocities at the end of the time periods. distance traveled feet Question Help: Video 20210110 2205M2 ing 20210110 220552 jpg

the motion of the particle is described by the equation x(t)=at^3-bt^2. where a is 3.36 in m/s^3 and b is 2.84 in m/s^2. find the instantaneous velocity in m/s of the particle from time t 5.93s. Express your answer rounded off to two decimal places. Do not include the unit.

The velocity of a rocket is given as a function of time by  v(t) = A(1 – e-bt) for 0 , t , 30 s, where the constants A = 150 and b = -0.15. [ d/dx (e-ax dx)  = -a e-ax;  ∫ e-ax dx = -1/a e-ax ] a) What are the SI units of A and b?   b) What is the speed of the rocket at t = 10 s?   c)Find the displacement of the rocket in the first 10 s ( from t = 0 s to t = 10 s)

At t = 0, a train approaching a station begins decelerating from a speed of 80 miles/hour according to the acceleration function a(t) = -1280(1+ 8t)-3, where t> 0 is measured in hours. The units of acceleration are mi/hr2. (a) What's the velocity of the train at t: 0? (b) Find the velocity v(t) of the train for t > 0. (c) How far does the train travel in the first 15 minutes (1/4 hour)?