At time t = 0 s, an object is observed at x = 0 m; and its position along the x axis follows this expression: x = –4t + t2, where the units for distance and time are meters and seconds, respectively.  What is the object's average speed between t = 0 s and t = 3.0 s ?

Given v(t) = 21 + 20 t, where v is in m/s and t is in s, use calculus to determine the total displacement from t₁ = 1.5 s to t₂ = 3.1 s. Express your answer using two significant figures.

A space probe on the surface of Mars sends a radio signal back to the Earth, a distance of 6.65 ✕ 107 km. Radio waves travel at the speed of light (3.00 ✕ 108 m/s). How many seconds does it take for the signal to reach the Earth?

The velocity of a toy car moving along as straight path is shown in the figure. Match the numbers according to the graph. Assume the numbers in the choices are followed by proper units (not shown), i.e., distance in [m], speed or velocity in [m/s], and acceleration in [m/s^2].

The speed of an object as a function of time is given by the following equation: What is the magnitude of the object's acceleration (in m/s2) at t = 5 s? X 32

The x component of the velocity of an object moving along the x axis is given as vy = 4t – 3t where vy is in meters per sec and t in seconds. The x component of its average velocity over the interval of time from t =0 to t= 2 sec is: O -2m/s O 2 m/s O -4m/s

An object's position in the X-direction as a function of time is given by the expressio%3B x(t) = 5t2 + 2t where are quantities have proper SI Units. What is the object's average velocity in the x-direction between the times t = 1.71 s and t = 2.37 s. Just enter the number rounded to 3 significant figures and assume it has proper SI Units.

The acceleration of a particle is a constant. At t = 0 the velocity of the particle is (15.8î + 18.4ĵ) m/s.At  = 3.6 s the velocity is 10.5ĵ m/s. (Use the following as necessary: t. Do not include units in your answers.)   (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin.

A remotely controlled toy car travels along a straight line and its position changes with time following the law: x(t)=51³-1²+1 where time t is measured in seconds and the coefficients have such dimensions that the position x(t) is measured in meters. 10. What is the displacement of the car for the first 2 seconds since the start at t=0 s? 11. What is the average velocity of the car for the time period between the t=0s and t=2 s? 12. What is the instantaneous velocity of the cat at t=2s ? 13. What is the instantaneous acceleration of the car at t=2 s?

The expression x = 9.40 cos(2.25(PI)t + (PI)/2) describes the position of an object as a function of time, with x in centimeters and t in seconds. What are the following? (e) position of the particle at t = 1.50 s ________cm