A rocket's position (in meters) as a function of time (in seconds) is given below. Round all answers in this problem to one decimal place r = (t²- 3t)i + (t³ + 3)ĵ (a) What is the magnitude of the rocket's (in m/s) velocity at t = 2.5 s? (b) In what direction is the rocket moving (in degrees) at t = 2.5 s? (c) What is the magnitude of the rocket's acceleration (in m/s²) at t = 2.5 s?

The velocity of an object is given by, = u + at V ds dt. where, u is the initial velocity, a is the acceleration, and ₺ is the time in seconds. Solve the differential equation to obtain the displacement, s, given that at t = 0, s = 7 (metres) : 1 if u = 3 ms ¹, a = 2.4 ms 2, calculate the displacements at t = 4.9 seconds. Give your answer to 2 decimal places.

The position of an object in circular motion is modeled by the given parametric equations, where t is measured in seconds. x=7sin((pi/8)t), y=-7cos((pi/8)t) How long (in sec) does it take to complete one revolution?

Can you go step by step.

A piece of wood moves at a velocity (measured in millimeters per year) of v(1) = r² – 3t – 4 where 1 = 1 would be the end of the first year. If a is the displacement of the wood in the first 5 years and b is the distance traveled in the first 5 years, what is a- b? None of the listed answers

v sin 20 gives the distance x travelled (in feet) by a projectile launched from 32 The formula r% = the ground, with initial velocity v (in feet/sec) and initial angle 0 (in radians or degrees). a. Write an expression for the total differential in x. b. Use the total differential to estimate the error in calculating the range of a projectile with initial velocityv 100 ft/sec and initial angle 0= 50 degrees, with measurement errors of dv = t10 ft/sec (for velocity) and d6==5 degrees (for the initial angle). (Note: remember to use radians for the differential in 0.)

help answer please.

I need help with this practice problem. I was given the answer key but I need help solving it step by step.  A car drives North for 1 km. Then it turns and drives 2 km at 30◦ South of West.Finally the driver turns again and drives 0.5 km Northwest.(a) What is the total distance driven?(b) What are the magnitude and direction of the car’s overall displacement? Answer Key: a.) 3.5 km b.) .11 km, 9.55◦

A bear, searching for honey wanders 30 meters south, then 15 meters west. Frustrated, he wanders another 14 meters north and then 5 meters east. Calculate the magnitude of bear's displacement. Round the answer to three significant figures.

Bicyclists in the Tour de France reach speeds of 500 miles per hour (mi/h) on flat sections of the road. What is this speed in kilometers per second (km/sec)? cf. 1 mile = 1.609 km